Tài liệu Bí quyết ôn luyện thi đại học đạt điểm tối đa vật lý tập 1 - lê văn vinh
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Tham gia: 02/08/2015
Mô tả:
ThS.
L EVAN VINH
G I A O V I E N C H U Y E N L U Y E N T H I D A I HOC
Bl QUYET ON LUYEN THI DAI HOC DAT DIEM TO'I DA
VAT L I
TAP 1
THEO TtfNG o n j Y f i N D 6
vA GiAi a n TI6T
Bien soon theo cau true de thi cua Bo Giao Due va Dao too
(Tdi ban tan thA nhcU c6 sita chSa va bo sung)
- Tuyen tap cac bai toan cd ban, hay la va kho
- Tong hgfp cac phiiang phap giai nhanh nhat khi lam bai trac nghiem
- Sach danh cho hoc sinh luyen thi Dai hoc - Cao dang
NHA AUAT BAN DAI H O C QUOC GIAH A NQI
NHr^ x u n r B A N D R I H O C O U O C c m Hf^ N O I
16 H d n g C h u o i - H a i B d TrUng - H d N p i
D i e n t h o a i : B i e n t a p - C h e b a n : (OA) 3 9 7 1 4 8 9 6 :
H d n h c h i n h : C04) 3 9 7 1 4 8 9 9 ; T o n g b i e n t a p : ( 0 4 ) 3 9 7 1 4 8 9 7
L a m g i de c6 d u o c d i e m 10 m o n Vat ly? De thoi, neu d o la d i e m 10 t r o n g t h i
tot nghiep. Vay t h i cao dang t h i sao! Co de n h u tren khong? N o i c h u n g la cung
Fax: (04) 3 9 7 1 4 8 9 9
k h o n g k h o l a m . The con d i e m 10 trong de t h i dai hoc t h i sao! C o k h o l a m
Chiu
trdch
nhiem
khong? T a i day chac nhieu ban da c6 cau tra l o i r o i ! D a so nhieu ban cho rang
xuat ban
dieu nay la qua k h o va k h o n g the l a m duac. T u y nhien ben canh d o cijng c6
Gidm
doc - Tong
bien
tap :
TS. PHAM THj TRAM
nhieu ban cho rang cijng k h o n g c6 g i kho l a m va hoan toan c6 the l a m dugc
neu CO n h i r n g b i quyet o n luyen t h i bo ich truoc k h i buoc vao p h o n g thi. C u o n
Bien
CONG TY KHANG VIET
Che ban
Trinh
sach nay la d a n h cho cac ban n h u the va ciang danh cho cac ban c6 nit.:-,i t i n la
THU LUYEN
tap
CONG TY KHANG VIET
bay bia
m i n h se l a m d u o c dieu m o n g uoc do. Co so de t i n vao dieu nay la t r o n g k h u o n
kho cua de t h i k h o n g c6 cau nao qua k h o n h u ben de t h i toan. Vay cai k h o 6
day la gi? D o chinh la t h o i gian l a m bai. T r o n g de t h i c6 tong cong 50 cau
n h u n g chi c6 90 p h i i t v i the chia ra t h i 1 cau chi c6 108 giay (1,8 p h i i t ) . Vay b i
Tong phdt
hdnh
vd dot tdc lien ket xuat ban:
C O N G T Y TNHH MTV
DjCH V g VAN HOA K H A N G V I | T
Dia ch?: 71 Dinh Tien Hoang - P.Da Kao - Q.1 - TP.HCM
Dien thoai: 08. 39115694 - 39105797- 39111969 - 39111968
Fax: 08. 3911 0880
Email: khangvietbookstore©yahoo.com.vn
Website: www.nhasachkhangvlet.vn
quyet nao d e g i a i bai toan k h o khan 6 tren?
Bi quyet d a u tien de c6 d i e m 10 la phai bie't phan loai cap d o cau hoi va sau
do de l a m truoc, k h o l a m sau.
Bi quyet t h u hai la phai lam duoc n h u n g cau k h o dugc p h a n loai 6 tren
trong thai gian cho phep. De l a m dugc dieu nay d o i hoi cac ban phai giai dugc
that nhieu bai tap va phai phan ra t u n g chuyen de cu the de bie't bai toan giai
quyet theo h u o n g nao. N h u vay de giai quyet cac bai tap thugc d a n g k h o nay
cho nhanh va c h i n h xac nhat la n h i i n g g i cuon sach l a m dugc. V i the'de thuc
hien dugc b i quyet t h u hai t h i can l a m dugc n h i i n g viec sau:
1. Su d u n g thanh thao m o i lien h? giira dao d o n g dieu hoa v o i chuyen dgng
tron deu va cong cu de l a m dugc viec tren chinh la vong tron lugng giac. K h i
SACH L I E N K E T
sir d u n g v o n g t r o n l u g n g giac, cac bai toan n h u ve pha, thai gian, quang
Bf Q U Y E T ON LUYEN THI DAI HQC DAT DIEM TOI DA VAT U -
d u o n g ... dugc giai quyet true quan de hieu va it t o n t h o i gian (thi trac nghiem
TAP 1
can dieu nay nhat).
2. Phai s u d u n g tot kien thuc h i n h hgc phang de t i m d o I o n cac dai l u g n g
M a so: 1 L - 5 3 1 D H 2 0 1 3
Ma so ISBN:
vecto. T r o n g c h u o n g dao d g n g co t h i can n a m va ap d u n g d u g c d i n h ly h a m so
978-604-934-857-0
In 2.000 cuon, kho 1 6 x 2 4 c m
sin va cosin de t i m bien d o va pha ban dau cua dao d g n g tong h g p . Ben
- •
c h u o n g d o n g dien xoay chieu la can nhat v i cac h i n h phang 6 day dugc ve t u
Tai: Cty TNHH MTV IN AN MAI THjNH DLfC
phuang phap vecta trugt. D e giai tot cac bai tap t r o n g c h u o n g nay p h u o n g
Dia c h i : 7 1 , Kha Van ^ a n , P. Hiep Binh Chanh, Q . Thu Dufc, TP. H o Chi M i n h
So xuat b a n : 2033 - 201 3/CXB/03 - 2 8 4 / D H Q C H N
ngay 31/12/2013.
Quyet d i n h xuat b^n so: 5 4 3 L K - T N / Q D - N X B D H Q G H N , cap ngay 31/12/2013
In xong va n o p lOu c h i e u quy I n a m 2 0 1 4
phap vecto t r u g t k h o n g the k h o n g bie't t o i .
'
3. Sir d u n g thanh thao may t i n h cam tay (Fx 570 ES hoac Fx 570 ES PLUS).
T r o n g t i n h toan b i n h t h u o n g ma cac ban k h o n g c6 thao tac n h a n h tir chie'c ma>
tinh thi se mat kha nhieu thoi gian. Ngoai ra, chirc nang ciia cac chie'c may t i n t
vugt
nay con
xa su mong dgi cua chiing ta, no c6 the giai
ne'u dua ve chedo phuc.
dugc
nhieu bai toan
^hdn
1:
DAD
B O N G CII^U HdA
XO
LY T H U Y E T
4. Nam chac cau true de thi de on diing trpng tarn, khong lang phi thoi gian
I. D A O D O N G C O
1.
Thendolddaodongca?
on nhiing kien thiic khong ra thi. Ne'u cac ban hpc ben ban co ban hoac khong
muon hoc chuong chuyen dong ciia vat ran ben ban nang cao thi cac ban nen
Dao dpng co la chuyen dpng qua lai quanh mpt v i tri dac bi§t gpi la vj tri
can bang.
chQn ban co ban ma thi. De thi cho chiing ta chon mpt trong hai phan nhung
chiing ta nen chpn ngay tix dau l u y f n thi chii khong de vao phong thi moi
2, Dao dong tudn hodn
chpn. Ne'u cac ban chac chan chpn ban co ban (da sochpn ban nay) thi cac ban
khong hgc cac kien thiic sau: nguyen chuang chuyen dpng cua vat ran, nguyen
-
Dao dpng tuan hoan la dao dpng ma trang thai chuyen dpng ciia vat
dupe lap lai nhu cij (vi tri cii va huang cu) sau nhiing khoang thoi gian
bang nhau.
-
Dao dpng tuan hoan don gian nha't la dao dpng dieu hoa
chuong tix vi mo den vT mo. Khong hoc phan hieu ling Doppler, con lac vat ly>
cac bai toan ve mac hinh sao, tam giac trong dong dien xoay chieu 3 pha, cac
bai toan ve thoi gian dao dong, so dao dpng, quang duong vat dao dpng dupe
trong dao dpng tat dan, cac cong thiic Einstein trong chuong lupng t u anh
II. P H l / O N G T R I N H C U A D A O D O N G D I E U HOA
sang, cac bai toan ve thay doi chieu dai, thoi gian trong thuye't tuong doi, cac
1. Vtdu
bai toan giao thoa anh sang bang cac dung cu quang hpc. Cac phan nay chi ra
-
Gia su M chuyen dpng ngupc
duong van toe goc la co, P la hinh chieu
bi phan tam va mat thoi gian.
ciia M len Ox.
5. Nho cong thiic. Chiing ta khong the diing cong thiic nao ciing d i chiing
y
chieu
ben ban nang cao v i the chiing ta phai loai bo ngay cac kien thiic nay de khong
/
cot -fj
Tai thoi diem t = 0, M co tpa dp goc (p
minh ma tot nha't la trong qua trinh hpc hay chiing minh va nho no de lam bai
Sau thoi diem t, M co tpa dp goc (ro.t + cp)
t^p moi nhanh dupe.
Khi do: OP = x => diem P co phuong trinh la:
6. Phai biet tinh nham cac bieu thiic tinh co ban nhu cos—= 0;cos —= —...
2
3
2
nhfmg cai nay nham nhanh hon may tinh nhieu. Phai thanh thao may tinh cam
tay nhung dung de phu thupc vao no.
7. T u tin va kien tri on luy^n, nha't dinh cac ban se thanh cong.
Tac gia
X = OMcos(cot + (p)
-
Nhd Sdch Khang Viet xin trdn trgng gi&i thi^u tai Quy doc gid vd xin
lang nghe tnoi y kien dong gop decuoh sdch ngdy cdng hay han, boich han.
-
Email: khangvietbookstore@yahoo.com.vn
Do ham cosin la ham dieu hoa nen diem P dupe gpi la dao dpng dieu hoa
Dao dpng dieu hoa la dao dpng trong do l i dp ciia vat la mpt ham cosin
(hay sin) ciia thoi gian.
3. Phuong trinh
-
Cty T N H H Mpt thanh vien - Dich V u Van Hoa Khang Vi?t.
Tel: (08) 39115694 - 39111969 - 39111968 - 39105797 - Fax: (08) 39110880
' '
2. Dinh nghia
ve:
71- D i n h Tien Hoang, Phuang Dakao, Qu|n 1, TP H C M .
Dat A = O M t a c 6 : x = Acos(co.t + (p)
Trong do A, w, cp la hang so
Le Van Vinh
Thuxingtti
V A CDN LAC L d
4.
Phuang trinh x = A cos(co.t + (p) gpi la phuong trinh ciia dao dpng dieu hoa
*
A la bien dp dao dpng va la li dp cue dai ciia vat. (A > 0).
*
(co.t + (p) la pha ciia dao dpng tai thoi diem t
*
cp la pha ban dau tai t = 0 ((p > 0;(p = 0;(p < 0)
Chuy
a) Diem P dao dpng dieu hoa tren mpt doan thang co the coi la hinh chieu
ciia diem M chuyen dpng tron deu len duong kinh la dogn thang do.
b) Ta quy uoc chon true x lam goc de tinh pha aia dao dong va chieu tang cua
pha tuong ling voi chieu tang ciia goc MOP trong chuyen dong tron deu.
I I I . CHU K I , T A N SO, T A N SO GOC CUA DAO D Q N G DIEU HOA
1. Chu ki va tan so
Khi vat tro ve vi tri cii, huong cii thi ta noi vat thuc hi^n 1 dao dong toan phan.
*
Chu ki (T): ciia dao dong dieu hoa la khoang thai gian de vat thuc hien
mpt dao dong toan phan. Don vj la s
*
Tan so (f): cua dao dong dieu hoa la so' dao dong tuan hoan thuc hien
trong mgt s. Don vi la 1/s hoac Hz.
Neu keo vat khoi vj tri can bang va buong ra vat se dao dong quanh vi tri
can bang, gii>a hai vj tri bien
V I I . K H A O SAT DAO D Q N G CUA CON LAC LO XO VE M A T D Q N G
LI/C HQC
Xet vat 6 li dp x, 16 xo gian mot doan Al = x. Luc dan hoi F = - k A l
Tong luc tac dung len vat: F = -kx
•k
Theo dinh luat I I Niu ton: a =
x
m
Dat co^ = k/m => a + co^x = 0
Trong dao dong dieu hoa o) dupe gpi la tan so goc.
Giiia tan so'goc, chu ki va tan so c6 moi lien he:
Tan so goc: (» = . —
m
= 27lf
T
IV. V A N TOC VA GIA TOC CUA DAO D Q N G DIEU HOA
1. Van toe
*
Chu ki:
*
Luc keo ve
-
Van to'e eiing bie'n thien theo thoi gian
*
Tai
*
Tai
X
= ±A thi v
=
0
X = 0 thi V = vmax =
to.A
2. Gia toe
Gia to'c la dao ham ciia van to'e theo thoi gian
a = v ' = x" = -co^A cos(a)t + c}))
a = -LoH
*
Taix = Othia = 0
*
Tai
X = ±A
thi a = am.ix = co^A
V. DO T H I CUA DAO D Q N G DIEU HOA
Do thi ciia dao dpng dieu
hoa vai cj) = 0 c6 dang hinh
sin nen nguai ta con gpi la
dao dpng hinh sin.
V I . CON LAC L 6 XO
Con lie 16 XO gom mot vat nang m gan vao 1 dau ciia 16 xo eo dp eung k
va khoi lupng khong dang ke. Dau eon lai eiia 16 xo eo dinh.
Con lac CO 1 v i tri can bang ma khi ta tha vat ra vat se dung yen mai.
F
M.
Luc huong ve vi tri can bang gpi la luc keo ve. Luc keo ve c6 dp Ion ti le
Van toe la dao ham ciia l i dp theo thoi gian:
V = x' = -coA sin(a)t + cj))
.j't!:i
Vay dao dpng eiia con lac 16 xo la
dao dpng dieu hoa.
2. Tan so goc
CO =
'
voi li dp va gay gia toe cho vat dao dpng dieu hoa.
V I I I . K H A O SAT D A O D Q N G CUAA LO XO VE M A T N A N G L l j Q N G
1. Dong nang cua con lac Id xo: W^j = ^ mv^
2. The nang eua con idc Id xo: Wt = - kx
-
. T
The'nang va dpng nang ciia con lac 16 xo bien thien dieu h6a voi chu ki —
3. Co nang eua con idc Id xo. Su bdo toan eo nang
2
2
2
2
Co nang ciia con lac ti le voi binh phuong voi bien dp dao dpng
Co nang ciia con lac 16 xo dupe bao toan neu bo qua mpi ma sat.
N h a n x e t q u a n t r o n g : dis'dat diem cao phan nay thi hi quyet dau tien la
cdc ban phdi su dung dwgc duang tron htgng gidc thuan thuc vd sau day la hi
quyet thu nhat.
' '''''
"'
5
S a u d a y l a p h u o n g phap khac rat t r y c quan, the hien d u g c mo'i q u a n he
Chuyen de 1
giira cac dai l u g n g n h a m g i i i p cac ban t r o n g vi#c giai n h a n h nha't, c h i n h xac
nha't cac dang toan ve dao d o n g co, song co, d o n g d i e n xoay chieu va dao
D U O N G T R 6 N LUgrNG GlAC TRONG DAO D O N G Bltu H6K
d g n g t r o n g mach L C . co the n o i rang: p h u o n g phap d i i n g d u o n g t r o n l u g n g
I. KHO KHAN KHI G I A I BAI TAP:
giac quye't d i n h I o n den viee dau hay rot ciia cac ban.
So l u g n g cong t h u c yeu cau cac ban n h o van d y n g t r o n g c h u o n g dao d g n g
II. PHl/CNG PHAP
CO rat n h i e u chi t i n h p h a n to d a m , bat bugc la 16 cong t h i i c n h u n g v o i so'
Bieu d i e n ca ba h a m l i d g (x), v a n toe
l u g n g cac cong thuc d o cung chi giai quye't d u g c cac cau h o i rat co ban,
(v) va gia toe (a) va k h i can ta co the
k h o n g the giai quye't d u g c he't cac dang bai tap dat ra cua c h u o n g nay. O
bieu d i e n lire tren c i i n g m g t d u o n g
phan dao d g n g kie'n thuc toan lien quan la cac cong t h u c l u g n g giac va giai
cac p h u o n g t r i n h l u g n g giac day la kho khan I o n do'i v o i da so' cac ban ke ca
cac ban kha g i o i v i ra't hay sot n g h i ^ m b o i t i n h lap lai cua h a m t u a n hoan.
t r o n l u g n g giac n h u sau:
+
L i dp: X = A cos(cot + cpx) la h a m cosin
D u o n g t r o n l u g n g giac v o i vi^c lien he giira chuyen d g n g t r o n deu v o i dao
=> c i i n g chieu true cosin co chieu (+)
d g n g d i e u hoa se giai quye't n h i i n g kho khan tren m o t each de dang.
tir trai sang p h a i v o i bien d g la => x^^^^ = A
H i e n tai tren d u o n g t r o n l u g n g giac da so' chi s u d u n g m o t true cosin cho
+
p h u o n g t r i n h dao d g n g x = A cos(cot + (p^) (true Ox) va cac dang toan c h u o n g
V a n toe tijfc thai: v = -A(osin(cot + cpx) la h a m trir sin
=> ngugc chieu true sin nen co chieu (+) h u o n g tir tren xuo'ng v o i bien d g
nay t h u o n g can c i i vao cac d\x kien bai toan cho t u p h u o n g t r i n h dao d g n g
v^ax^^-'^-
d a n g X = A cos(cot + (Px), de t i m chu k i , tan so', d u o n g d i , k h o a n g t h o i gian
D i e u nay
tuong duong
voi ham
v = Acocos(cot + (Pv)
voi
de d i t u toa d g xi den toa d o xi, t i m van toe, gia toe tai m g t t h o i d i e m nao
do, khoang t h o i gian 16 xo nen, gian ...
T u y nhien se kho khan cho cac ban k h i gap phai loai cau h o i dv! kien bai
+
=> ngugc chieu true cos co h u o n g (+) tir phai sang trai v o i bien d o a^^ =cf^A
toan k h o n g cho p h u o n g t r i n h dao d g n g dang l i do x = Acos((ot + cp^) ma
cho dang v a n toe tue t h a i v =-A(osin(cot + (Px)hoac cho d a n g gia toe tiic
D i e u nay t u o n g d u o n g v o i ham: a = a)^Aeos(cot + (Pa) v o i (pg = (p^, + ^ = (px + Ji
t h o i a = -(a'^Acos((ot + (Px) • Luc nay hau he't cac ban deu b i d g n g k h o n g the
bieu d i e n h a m (v) va h a m (a) tren d u o n g t r o n l u g n g giac.
T h o n g qua each bieu d i e n nay ta tha'y mpt so diem dac bi?t, vung dac biet
M u o n bieu d i e n d u g c tren d u o n g tron l u g n g giac t h i p h a i t u h a m (v), (a)
va m o i q u a n he ve pha ciia l i d g (x), van toe (v), gia toe (a) cung n h u viee
vie't lai d a n g h a m (x) bang each lay tich phan bac nha't h a m v a n toe (v) hoac
khai thae cac kien thuc l y thuye't lien quan ve dao d g n g dieu hoa, cac dang
bae 2 h a m gia toe (a) day la each rat kho k h a n cho cac bah v i sang hge k y 2
nang l u g n g ciia dao d g n g dieu hoa dugc the hien m g t each true q u a n tren
cac ban m d i d u g c hge n g u y e n h a m va tich phan. Vay giai phap nao c6 the
h i n h ve v o i m g t vai v i d u sau:
giai quye't cac k h o k h a n neu tren?
+
Bon vi tri dac biet:
N h i e u y kien cho r i n g : N e u m u o n tranh dieu nay t h i p h a i n h o h a m van toe
•
V i tri bien duong I: (x^^x = A ; v = 0; a = -co^A)
=> The'nang cue d a i , d g n g nang cue tieu
(v) som pha h o n l i d g (x) 1 goc ^ , con h a m gia to'c (a) ngugc pha v o i h a m l i
d g (x) t u y nhien, vi^c giai cac p h u o n g t r i n h l u g n g giac lien q u a n dieu nay
m a t n h i e u t h o i gian, chua m u o n noi d g chinh xac v o i da so cac ban la rat
6
G i a toe tuc thoi: a = -a)^Aeos((ot + cpx) la h a m trir cosin (ngugc h a m x)
-
V i tri can bang I I :
(x=0;
v = -coA;
a=0)
tha'p. K h o n g the n h o he't cac cong thuc, cac m o i quan he p h u c tap cua cac
=> The'nang cue tieu, d o n g nang eye dai
dai l u g n g co hge, v i thie'u t i n h true quan, thie'u m o i q u a n h ^ gSn bo giira cac
V i tri bien am I I I :
h i ^ n t u g n g vat ly nen t h u o n g tra l o i sai cac cau h o i d u co ban nha't.
(x = - A ; v = 0 ;
a^^^x =co^A)
I I I . CAC DANG TOAN
D a n g l : X a c d j n h c a c dai lUcfng li do, v a n toe, g i a t o e t a i thdi
d i e m t.
=> T h e n a n g cue dai, d o n g nang cue tieu
-
V j t r i can b i i n g I V : ( x = 0 ;
v^-,^=wA;
a = 0)
=> Tlie'nang cue tieu, d o n g nang cue dai
Kei luan: Vay dm ki dao dgn^ titan hoan cua ham dgn^ nang va ham thenang
cua
dao dong dieu hoa chi bang ^ chu ki T cua ham li do (x), khodng thai gian dedong
nang (the nang) tie cur dai thanh cite tieu hay ngugc lai la ~ chu ki T cua ham li
ga v i DU MAU:
V I d u 1 : M o t vat dao d o n g dieu hoa theo p h u o n g t r i n h x = 6eos(27tt)cm,
van toe ciia vat tai t h o i d i e m t = 7,5s la:
A. V = Ocm/s.
B. v = 75,4cm/s.
C. V = -75,4cm/s.
D . v = 6cm/s.
^hdn tich vd huong ddn gidi
do (x).
+
.. t\.
Bon vung dae biet:
D u n g true Ox bieu dien :
V u n g l : (x>0;
lue ban dau vat 6 v j t r i I sau t h o i gian
v < 0; a < 0)
=> vat chuyen d o n g nhanh dan theo chieu (-) v i a.v > O v a the nang giam,
t = 7,5s vat quay m o t goc:
d o n g nang tang.
cot = 271.7,5 = 1571 lap lai 7,5 v o n g
V u n g 2: (x < 0; v < 0; a > 0)
den v i t r i I I I => co van toe v = 0.
=> vat chuyen d o n g cham dan theo chieu (-) v i a . v < 0 va the nang tang,
C h p n dap an A
a
II
o
IV
d o n g nang g i a m .
V u n g 3: (x < 0 ;
V
v > 0; a > 0)
=> vat chuyen d o n g nhanh dan theo chieu (+) v i a.v > 0 va the nang giam,
d o n g nang tang.
V u n g 4: ( x > 0 ;
v>0;
d o n g nang g i a m .
Mo'i quan he vepha eua li do (x), van toe (v),gia toe (a): Qua h i n h ve nhan
tha'y d u g c m o i quan he ve pha ciia ham l i do (x), van toe (v) va gia toe (a) la:
9v
= gia toe (a) som pha h o n van toe (v) m o t goc ^ va s o m pha h o n l i do (x)
m o t goc 7t hay ngugc pha v o i l i do (x)
2y
cm.
A . a = Ocm/s2
B. a = 946,5em/s2.
C. a = -947,5cm/s2
D . a = -946,5cm/s2.
'Phdn tich vd hu&ng ddn gidi
D i i n g true Ox bieu dien
De cho h a m x dang sin can
chuyen
sang cos c6 dang: x = 6cos(47it) cm
(Pa = (p^ + ^ - (p, + 71
=> van toe (v) sam pha han l i d o (x) m o t goc
Vl d u 2: M o t vat dao d o n g dieu hoa theo p h u o n g t r i n h x=6sin
gia toe ciia vat tai t h o i d i e m t = 5s la:
a < 0)
=> vat chuyen d o n g cham dan theo chieu (+) v i a . v < 0 va the nang tang,
+
;
=> ban dau vat 6 v j t r i I sau thoi gian
t = 5s vat quay 1 goc o)t - 4n.5 - 20n
lap lai 10 v o n g den v j t r i cij.
=> CO gia toe a = -co^A = - 9 4 7 , 5 ^
s
C h g n dap an C
Vl d u 3 : M o t chat d i e m dao d o n g dieu hoa theo t c6 p h u o n g t r i n h van toe
v = 107reos 27rt + - em/s, toa dp ciia chat d i e m tai thoi d i e m t = 1,5s la
V
2J
_ A . x = l,5cm.
B. x = -5em.
C. x= + 5cm.
D . x = 0cm.
9
Cty n V H H M T V D W H JOtang
'Phdn tich vd hitang dan gidi
Bl/ofC 3 : Bieu d i e n dao d p n g dieu hoa tren d u o n g t r o n . Vat d i tir v i t r i X j
= 5cm
Bien d p A =
CO
den X2 t u o n g u n g v o i m p t chuyen d p n g t r o n deu d i tir M deh N v a i v a n
271
D u n g true O v bieu d i e n :
toe goc CO, ban k i n h la A .
L i i c ban d a u vat a v i t r i I sau t h o i gian
CO
= - A = - 5cm.
m
C h p n dap an B
Vl d u 4 : Van toe cua m p t vat dao d o n g d i e u hoa bien t h i e n theo t h o i gian
theo p h u o n g t r i n h v = 27:cos 0 , 5 7 : t - - (cm/s). Vao t h a i d i e m nao sau
6y
v i DU
Vi d u
MAU:
1 : Vat dao d p n g d i e u hoa v o i p h u o n g t r i n h x = Acos(cot + cp) (cm).
T i n h t h a i gian ngan nhat vat d i t u :
A
a) V j t r i can bang den v i t r i x = — .
day vat qua v i t r i c6 l i d p x=2cm theo chieu d u o n g cua true tpa d p .
A.8/3S
B.2/3S
^hdn
Bien d o A = ^ ^
CO
= — =
0,5Tt
C. 2s
D . 4/3s
tkh vd hii&ng dan gidi
4cm
b) V i t r i can bang den v i t r i x =
c) V j t r i can bang den v j t r i x =
^hdn
(POv
sau t h a i gian t v a t quay 1 goc
2
A^f3
tich vd hu&ng ddn gidi
A
=-7
a) K h i vat d i tir v j t r i can bang den ^ = y ,
o
^Ov =
t u o n g u n g v o i vat chuyen
d p n g tren
d u o n g t r o n t u M den N d u o c m p t goc
a = cot = 0,57rt = — v i c6 l i d p x = 2cm,
3
Acp n h u h i n h ve ben.
bien d p A = 4 cm va c h u y e n d o n g theo chieu {+) den v j t r i V I
De thay: sin Acp = ^ => Acp =
=> mat t h o i gian t = 2/3s. C h g n dap an B
=> K h o a n g t h o i gian ngan nhat de vat d i t u
Dang 2: Xac d j n h t h d i g i a n v a t d i tuT vj t r i x j den v i t r i x j :
Phi/cTng p h a p g i a i :
Cho p h u o n g t r i n h dao d p n g vat c6 dang:
X = Acos(cot + (p)cm
BUdc 1 :
(v;>0;
Xac d i n h v j t r i X j tren d u a n g
Bl/dc 2:
Vj<0;
hay
>0;
Xac d i n h v j t r i X2 tren d u o n g
V2
<0;
la: At =
CO
d p n g cua
hay V2 = 0 ) .
AV2
rad.
n
6
T
27t
12
T
bang
den
^
,
-, t u o n g u n g v o l vat chuyen
T h a i gian v a t d i t u v i t r i X j den X2 la : At = — .
lap lai 1,5 v o n g den v i t r i I I I
X
«,
Slide 4 : Xac d j n h goc cp = M O N .
t = 1,5s vat quay 1 goc cot = 2 i i . l , 5 = 3n
=> CO toa d o
Vift
vat
^
d u p e m p t goc Acp n h u h i n h ve ben.
De thay: sin Acp = — => Acp = - rad.
2
4
^
V
I—
=i> K h o a n g t h o i gian ngan nhat de vat d i t u VTCB deh x = — — la:
Bi qtiyei on luyen thi dai hoc dat diem toi da Vat It, tap l~Le
At =
Van Vinh
Cty TNHH MTV DWH
Tit hang nay, ta sc gicii qiii/ct nhi'mg bai tocin vc thai gian trong dao dong dieu hoa
mot each nhanh nlid't neii dccho diem di va diem den dqc bict nhu tren.
Acp
CO
8
2n
T
c) K h i vat d i tir v i t r i can b^ng den x =
BAI TAP VAN DUNG:
p
, t u o n g l i n g v a i vat chuyen dpng
tren d u o n g t r o n t u M den N duoc m o t goc Acp n h u h i n h ve ben.
C a U 1: Vat dao d o n g dieu hoa v o i p h u o n g t r i n h x = Acos(cot + cp) (cm). T i n h :
a)
Thoi gian ngan nhat vat d i t u v i t r i c6 l i do X| =
vat d i t u V T C B den x =
At =
Acp
CO
n
_3_
2n
I
• •
A
b) Thoi gian ngan nhat vat d i tif v i t r i c6 li do
la:
X2 =
6
t u o n g u n g vcVi vat chuyen d o n g tren
theo chic?Li am.
d) Thoi gian ngan nhat vat di tir vj t r i ccS l i dc) x, = -A
d u o n g t r o n t u M den N d u o c m o t goc
Acp n h u h i n h ve ben.
X2 =
AV2
den vj t r i c6 l i dc>
theo chieu am.
De thay: sin Acp = ^ => Acp = ^ rad.
'Phdn tick vd huang dan gidi
a) Khoang t h o i gian ngan nhat vat d i tir
=> K h o a n g t h o i gian ngan nhat de
vat d i t u V T C B den x = A la:
vi t n X, =
AV3
—
A
den ^2 = y
tuong
u n g vc>i vat chuyen dcing tren d u o n g
_^
^
tron tir M den N .
CO
Min t
T o m lai: ta c6 bang thoi gian trong dao dong dieu hoa sau:
-A
den v i t r i c6 l i dc)
A
X-, =
d) K h i vat di t u v i t r i can bang den x =
2
^\ —
' 2 •
AN/2
c) Thoi gian ngan nhat vat d i tir v i t r i c6 l i do x, = - ~
^
den vj t r i c6 li do
2
Av'3
T
Acp
At = -
den v i t r i c6 l i do
A
V3
Acp = — rad.
^
3
=> K h o a n g t h o i gian ngan nhat de
De thay: sin Acp =
Khang Viet
o
(
2
A
2
= t
Asfd.
=1
~ 6^
T_
12
>0
+ t,
0-^
2 ;
L-1
4
Ta bieu dien cac d i e m tren len true dao d o n g dieu hoa se thay ro h o n
T
~A
_AS
A42 _A
o
\
T_
6
•1
L
4
^
]
r
* '
A
Ayll A41
T
12
4
1 -x
Bf quyei on liiyen ilii dai hoc dat diem tot da Vat It, t^p 1-Le Van Vitth
d) Khoang thoi gian ngSn nha't v^t di tu vj
tri xi = - A den xj =
theo chieu
b) Khoang thoi gian ngan nha't vat di tij" vi
A ^
tri X j A
— den
= - —dirong
tuongtron
imgtixvoi
vat chuyen
dpngX2 tren
M
den N.
Min t (A A' = t
+ t 0-+
>0
I2 >—2,
I2
y
am tuong u n g voi vat chuyen dong tren
-A
d u o n g tron tu M den N.
^
AV2 ^ = t(~A->0) + t(O^A) + V
Aj2]
A—•—•—
2
I
T
4
~ 12 ^ 1 2 " 6
Bieu dien len tryc dao dong dao dgng dieu hoa
-A
O
T_
12
T
= —+ — +
A
2
L1 2
Ayfl AS
A^
A-Jl
fT
T\
4 U
8
_A
5T
A
A-JIAS
6
Tdi day ta da cd cdi nhin mai vedang todn th&i gian trong dao dong
dieu hoa, tif day ede bai vequdng duang, toe do trung binh, van toe trung binh... eo
the dime gidi qiiyet rat de dang.
Ket luan:
c) Khoang thoi gian ngan nha't vat di tvr vi tri
xi = A>/2
— den X2 = A- Vy 3theo chieu am tuong ung voi vat chuyen
dong tren d u o n g tron tu M den N.
+ t(O^A) + t
A>/2 A 7 3 1 = t
D a n g 3. B a i t o a n x a c d j n h t h d i d i e m v a t d i q u a v j t r i x d a b i e t
( h o $ c V, a, \Nt, Wd, F) I a n thuT N
PHl/QNG P H A P
* Trong mot chu ky T (27r) vat di qua x hai Ian neu khong ke den chieu
chuyen dpng, neu ke den chieu chuyen dong thi se di qua 1 Ian
* Xac dinh Mo dua vao pha ban dau (xo, vo chi quan tarn < 0 hay > 0 hay = 0)
* Xac dinh M d u a vao x (hoac v, a, Wi, WJ, F )
2 -
= 1 I fl_ll I I T
12
Bieu dien len true dao dong dieu hoa
-A
A42 A
^V3
T
8
O
A
2
A-Jl
A(p
Ap d u n g cong thuc t = (0
V
Liru y: De ra thuong cho gia tri n nho, con neu n Ion thi tim quy luat de
suy ra nghiem t h u N.
^
T
6
T
4
Thai gian dao dong cua vat dugc xdc dinh nhu a tren nhimg hinh ve duai eho edc
ban CO cdi nhin true quan hem
Cdc loai thucmggap vd cong thiic tinh nhanh
- Q u a X k h o n g ke den chieu
+ N chin: t = ^ ^ ^ T + t2 i h ^hoi gian de vat di qua vi tri x Ian thu 2 ke tu
thoi diem ban dau)
15
Bi 4ityet on luySn thi aai ntfcflflfaiem TOi aa var ii, lup I-LB
+
-
N le: t =
N - 1
van
vmn
T + t i (ti t h a i gian de vat d i qua v i t r i x Ian t h u 1 ke t u t h a i
N h ^ n xet: each tinh theo cac khoang thoi gian dqt Met tuy trinh bay tren giay thdy
nhieu ban nhung thuc tetinh thi rd't nhanh. Khi gidi chiing ta khong can ghi cu the
d i e m ban d a u )
md chi viec cong cdc khodng thai gian Iqi thoi.
Q u a X ke den chieu (+ ho|c - )
Cung bdi todn tren nhung neu thai diem di qua vat Id rdi l&n thi ta lam nhu vi du sau
t = ( N - 1)T + t j ( t i t h o i gian de v a t d i qua v i t r i x theo chieu d a u b a i quy
d i n h Ian t h i i 1 ke t u t h a i d i e m ban dau)
m vi D U
V I dy
V l dM 2: M p t v a t dao d p n g dieu hoa v o i p h u o n g t r i n h x = 4cos(47tt + — )cm.
6
T h o i d i e m t h u 2013 vat qua v i t r i x = 2cm.
1 : M p t v a t dao d o n g dieu hoa v o i p h u a n g t r i n h x = 4cos(47it + —)
6
c m . T h o i d i e m t h u 3 v a t qua v i t r i x = 2cm theo chieu d u a n g .
A.9/8S
B. l l / 8 s
C.5/8S
^- -IT'
D . 1,5 s
Cach 1 : G i a i theo p h u o n g trinh lugrng giac
Ta CO
x= 2
x = 4cos 4 7 r t + - = 2
6
lv>0^1
V = -167tsin
7l^
47rt+-
6J
= > 4 7 t t + - = — + k27t
6
>0
^ 24157
C.
s
24
3
'Phdn txch vd huang ddn gidi
47tt + — = - + k27:
6
3
t = A + ii (keN)
24
2 ^
'
47ct + - = — + k27t
6
3
t = - i + Ji ( k e N * )
8
2^
'
T h o i d i e m t h u 2013 (le) nen ta d u n g cong thuc: t =
= > t = - — + — k e N . T h o i d i e m t h u 3 l i n e v o i k = 3=> t = —s
8 2
^
8
,
Vay t i =
d u o n g la qua M 2 . Q u a M 2 Ian t h u 3 u n g v o i vat quay d u g c 2 v o n g (2T)
Vat qua v j t r i x = 2cm Ian t h u 2013 la :
6
(qua 2 Ian) v a Ian cuoi cung d i t u M Q den M 2 .
^
^
t=
t=^=Hs
8
Hoac t i n h theo cac khoang t h o i gian dat biet:
=
4V3
AV3 .
o
4
A
^ = - r - v a XM2 = 2 = - - 2
2
tM o ^ M 2 -VA../3
= 1 +1
6
I
(O^-A) + '(-A^O)
T _3T_3.0,5_3
4 ^ 4 ^ 1 2 "
4
~
4
+t
X
-A f
A
k
1
0
1 . .
2
24
2
24
N-1 ^ ^
T + ti
2
"
=
2013-1 1
2
1
.- +— =
2^24
12073
24
Cach 2 : S u d v n g duong tron lupng giac
Vat qua x = 2 la qua M i va M 2 .
-A
Vat quay 1 vong (1 chu k y ) qua x = 2 la 2 Ian.
Qua Ian t h u 2013 t h i phai quay
A^
0-»—
2y
1
24
— + - = — + - = —(s)
C h p n dap an A
Mo
CO
XMO
T + ti
dau u n g v o i k = 0 (nghiem tren).
Pha ban d a u (p = — nen ban d a u v a t 6 v i t r i M Q . V a t qua x = 2 c m theo chieu
3n
N-1
V o i ti la t h o i gian de v a t d i qua v i t r i x = 2cm Ian t h u 1 ke tir t h o i d i e m ban
C a c h 2 : S u d\ing d u o n g tron luQmg giac
Goc quet A(p = 2.2n +
D . D a p an khac
27T
271
1, ,
s)
C h u k y dao d o n g : T =: — = — = -- ((s)
CO
47t
2
CO
47t
Cach 1 : G i a i theo p h u a n g trinh lugtig giac
'Phdn txch vd huang dan gidi
x=2
^ 12061
B.
s
24
12073
MAU:
1006
v o n g r o i d i t u M o den M i .
M2
Goc quet Acp = 1006.271 + ^
.~8
^ t . 2 T . ^ , M = ll(s)?«^^''*-;
CO
24
24
T { ^ ' ; V;£f^ TiivH BiNH Vvwim
C h p n dap an A
16
17
Cty TNHHMTV
2 2
.2 -^0
T j r __T
6
12~12
T
0 5
12073
t = 1006T+ — = 1006.0,5+ — = - ^ = ^ s
12
12
24
^
m
- t 'A
= t
2012 vat qua v j t r i c6 v = -87t cm/s.
D . 1005,5s
B. 1005s
C. 2012 s
2T[
Theo bai ra ta c6: v = -167csin(27tt ~ ^ )
6
= ^ + k2n
6
t=- +k
6
= — + k27t
t= l . k
2
6
"^"^
•y
+12
la t h o i gian de vat d i qua v j t r i x = 2cm Ian t h i i 2 ke t u t h o i d i e m ban
2
^
^ N-2„
^
2012-2,
1
t=
T + t, =
.1 + - = 1005,5 (s)
^
2
2
- —
6
=> ban dau vat 6 M .
Vat qua v j t r i can t i m Ian t h u 2 tai P k h i d o
= ^^^I^T +1
^^Y^T +12
= 1005,5T = 1005,5(s)
A.
-s
8
B.
c. 5s
—s
24
^
'
D . 1,5s
8
'Pkan tich vd hu&ng ddn gidi
Cach 1: G i a i theo p h u a n g trinh lugng giac
I
2^ ^
Vat qua v i t r i x = 2cm Ian t h u 2012 la :
2
Pha ban dau cp =
1
2*2 2
Wd = W t r ^ - m c o ^ A ^ s i n ^ 2 7 r t - ^ = - m o ) A cos 2nt2
2
3^
t. =i + k = - + 0-i(s)
2
—
2
t r i vat d i qua la N va P.
t=
keN
d a u u n g v a i k = 0 (nghiem d u a i ) .
Vay
=> V =
Nhan xet: a day ta hieu dien duang tron theo v detinh nhanh han.
C a u 2: M o t vat dao d o n g dieu hoa v o i p h u a n g t r i n h x = 8cos(27it - —) cm.
3
T h a i d i e m t h u nhat vat qua v i t r i c6 d o n g nang bang the nang.
N-2,
Vat qua Ian t h u 2012 (chan) nen ta d u n g cong thuc : t = — ^ — T
Voi
2
Qua Ian t h u 2012:
Cach 1: G i a i theo p h u a n g trinh lugng giac
27rt —
-1
167r
vat quay d u o c n u a v o n g nen mat ^2
C h u k y dao d p n g : T = — = — = l(s)
6
-871
T
'Phdn tich ra hu&ng ddn gidi
2ni-^
Theo bai ra:
N h i n tren d u a n g t r o n ta thay v j
C a u 1: M p t vat dao d o n g dieu hoa vai x = 8cos(27it - —) c m . T h a i d i e m t h i i
6
CO
Khang Viet
T i n h theo van toe
V
B A I T A P VAN DUNG:
A . 1005,5s
+
DWH
o
sm
1-cos
2nt-^
3
2nt-^
= cos
3
3.
3
1 + cos 4 7 t t -
47tt
n
271^
V a y chpn dap an A
C a c h 2: S u diing d u a n g tron lug^ng giac
+
T i n h theo i i d o
Ta CO X =
A^-
= ±4%/3(c m .
cos
47tt-
2n^
A
.
.
= 0=>47it
7t ,
^
7
k
= — + k7r=:>t = — + — k e [ - l ; « . )
3
2
24
4
27t
T h o i d i e m t h u nhat u n g v o i k = - 1
t = —(s)
24^ '
rf ••^•Ii^,,..•
V i v < 0 nen vat qua M i va M2. Qua Ian t h u 2012
C h u y: vi thai gian khong nhan gia tri am nen thai diem thu nhat ung vai gia tri k
t h i p h a i quay 1005 v o n g roi d i t u Mo den M2.
nho nhat ma lam cho t > 0.
Goc que| A(p = 1005.271 + 71 => t = 1005,5 s .
18
19
Biquyet
on luyftt thi d^i hgc dat diem tot da Vat It, tap 1 - Le Van Vinh
D ? n g 4 . X a c d i n h s o I a n v a t d i q u a x t r o n g thcfi g i a n tu" t i d e n
tz ( A t = t 2 - t i )
Cach 2: S u dung duong tron lugng giac
x=±
Wd = W .
A
72
pHl/aNG PHAP
» Trong mpt chu ky T (27i) vat di qua x 2 Ian neu khong ke den chieu
chuyen dpng, neu ke den chieu chuyen dpng thi se d i qua 1 Ian
• CO 4 v i tri M i , M 2 , M a , M 4 tren duang tron.
Pha ban dau cp = — nen ban dau vat a
Mo
3
Thoi diem dau tien vat qua v i tri W d = W t
ling voi vat di t u M o den M 4 .
.
n
Goc quet: A(p =
n
n
^ A ( p l
= — =>t =
= —s
4
3
12
CO
*
Xac dinh M i dua vao ti v a PT x,v ( xi, v i chi quan tam < 0 hay > 0 hay = 0)
*
Xac dinh M dua vao x (hoac v, a, Wt, W d , F)
*
A p dung cong thuc A(p = coAt tim so'Ian
''
Cdc loai thudng gap va cong thuc tinh nhanh
Acp coAt
24
271
,i
= n,p(n + 0,p)
27t
Neu khong ke den chieu: N = 2n + N'
Cau 3:
Mot vat dao dpng dieu hoa voi phuong trinh x = 8cos(7rt - —) cm.
N' la so ian di qua x khi tren vong trong lupng giac quay dupe goc 0,p.27t
4
ke tir vi tri ban dau
Thoi diem thu 2010 vat qua vj tri c6 dong nang bSng 3 Ian thenang.?
Cach 1: giai theo phuong trinh lugng giac
Wd = 3Wt
^ sin
2.t-^ =
2
^
3
2,tt-^ = - ^
TTt-^
4
= 3cos^
>cos
4
k27i
t = —+ k k e N
12
+ k2K
t = - —+ k
12
Qua Ian thu 2010 (chin): t =
N-2
1
"2
Neu ke den chieu: N = n + N '
N' la so Ian di qua x theo chieu bai toan quy dinh khi tren vong trong
lupng giac quay dupe goc 0,p.27t ke t u vj tri ban dau
m vi D U M A U :
V i d u 1: Cho vat dao dpng dieu hoa theo phuong trinh:
keN
T + t, =
X = 3cos
2010-2 „ 11 12059
-.2 + — = .
(s)
12
12
4
A. 4
B. 5
=> CO 4 v i t r i tren duong tron M i , M2, M s , M4.
Vat qua vj tri x = 1,5 cm ta c6:
Qua ian thu 2010 thi phai quay 502 vong
3
cos
47tt--
(moi vong qua 4 Ian) roi di t u M o den M2.
Goc quet
4nt-^
=1004Tt +
.3
CO
12
.
12
4)
= > t = ^ = 1004.11 = l ^ s
20
C. 6
12
D. 7
Cach 1: Giai theo phuong trinh lugfng giac
2
A(p =^ 502.271 + 71 -
cm.
'Phdn tick vd hu&ng dan gidi
W , = iw=>x = ± '
47rt-^
3,
So Ian vat di qua v i tri x = 1,5cm trong 1,2s dau tien
Cach 2: S u d\ing ducmg tron lugfng giac
Wd = 3Wt
, ,...
3
= 1,5 => cos
= ^ + k2n
3
4 n t - i ^ = - ^ + 127r
3
3
t
2
3
1 k
= - + - (keZ)
6 2^
t =
l
(leZ)
Trong 1,2s dau tien tuc:
21
Bi(juyei
on
luyen
0 < t <1,2<=>
thi
itai hoc
itat dicin
0 < i + ii I - Le V&ti
-0,330
Goi M la v i t r i cua vat tai thoi diem t = 1,2s.
Goc ma vat quet dugc trong 0,2s la:
=^N' = 1 + 1 = 2 ii> N = 2.2 + 2 = 6.
n W H
mot dao dpng toan phan. Don vi la s
Bay gia ta tinh N ' .
Ta c6: BOM > AOB => vat di qua A
I
pHl/aNG PHAP
* Chu ki (T): cua dao dpng dieu hoa la khoang thoi gian de vat thuc hi^n
T -0,5s => At = 2T + 0,2 => N = 2.2 + N '
AOB = — r a d .
,
3
So sanh hai gia trj tren
/
v^
2
He thuc doc lap giua van toe va gia toe: A = — j - +
CO
CO
Chieu dai quy dao: S = 2A
m vi
DU
MAU:
Vi d u 1: (Trich de thi thu chuyen Nguyen Quang Dieu - Dong Thap Ian
1 nam 2013)
Mpt eon lac 16 xo dao dpng dieu h6a theo phuong n3m ngang c6 khoi
lupng m = lOOg, dp ciing k = lON/m. Keo vat ra khoi vj tri can bang mpt
khoang 2em roi truyen eho vat mpt toe dp 20em/s theo phuong dao
dpng. Bien dp dao dpng cua vat la:
A. 2^/2 cm.
B. V2 cm.
C. 4 cm.
D. 2 cm.
' ' '
^hdn tkh vd hit&ng dan gidi
Vai bdi todn nay chi can tim dugc tan so goc roi thd vao he thuc doc lap la cd ngay
bien do.
Tan so goc: co = . t =
Vm
i ^ . = lOrad / s
V0,1
Theo h ^ thuc dpc lap lien h^ giiia li dp va van toe:
22
9
A 22
==
Xx
2 2+ + 4 = 2 ' + ^
A
Chpn dap an A
co^
10^
= 8=^A = 2V2em
23
V l d u 2: (Trich de thi thu Nam T r ^ c - Nam D i n h Ian 1 nam 2013)
todn ve'luc, each gidi chung nhat Id tim hap luc tdc dung vdo vat gay ra gia toe
M p t vat dao d o n g d i e u hoa v o i gia toe cue dai amax va toe d p c^c dai Vmax.
Tan so dao d o n g la
£_
chuyen dong cho vat.
Cach giai bai nay n h u sau:
^max
g
£_
^max
Q f _ ^^-^max
-Q £ _
^max
Con lac dao d p n g tren doan thang dai 4cm chinh la q u y dao chuyen d p n g
ciia vat S = 2 A = 4 c m , v i the bien dp dao d o n g cua vat la A = 2cm.
K h i vat m dao dong, h o p luc cua luc d i ? n t r u o n g va luc dan h o i gay gia toe
^ h d n (icfi pd huang ddn gidi
a cho vat.
Bdi nay dan gidn chi Id tim moi lien he giua gia toe cue dai vd toe do cue dai.
Tai v i t r i bien, vat c6 gia toe cue dai. K h i do ta c6: Fd - Fdh = m.amax
Gia toe cue dai: a^^^ = co^A
qE - k A =
Toe dQ cue dai: v^^^
T u day ta lap t i le la eo ngay lien
a„.^^
o^A
(oA
e6n phia d u a l gan vat m . N a n g m len den v j t r i 16 xo k h o n g bien d a n g roi
tha nhe vat dao d o n g dieu h6a theo p h u o n g thang d u n g v a i bien do
V l d u 3 : (Trich de thi thu Nghi Lgc 4 - Ngh? A n Ian 1 nam 2013)
2,5cm. L a y g = lOm/s^. T r o n g qua t r i n h dao dong, t r o n g luc ciia m eo eong
M o t vat dao d o n g d i e u hoa tren quy dao dai 40em. K h i d o d a i la 10cm
vat CO van toe 2071V3 cm/s. Lay TC^ = 10. C h u k i dao d o n g cua vat la:
^hdn
C. 0,5s
A . 0,41W
C. 0,5W
D . 0,32W
ddn gidi
Day Cling la dang todn doc vdo rat la, tuy nhien degidi quyel bdi todn ndy cdc ban chi
can nha vecong thiec tinh eong suat ciia luc md da hoc tie cdc lap dual. P^^ = F.v
Vai F Id luc tdc dung vdo vat, v Id van toe chuyen dong ciia vat.
K h i do d a i vat la lOcm nen l i dp x = ± 1 0 c m
Trong dao dong dieu hoa, van toe chuyen dong cua vat Id van toe tiec thai nen eong
De cho q u y dao dai S = 2 A = 40 ^ A = 20cm
suat ciia luc cung Id eong suat tiec thai.
A p d u n g he thuc doc lap lien he giira l i do va van toe
Sau day la each giai cu the bai toan nay:
207t73
- = 1=>C0 = -
(coAf
B. 0,64W
E = 2.10^ V / m
V l d u 5 : M 6 t eon lac 16 xo c6 do c u n g k = 4 0 N / m dau tren d u p e giir eo d j n h
271 v „ 3 ^
B. I s
A = m. — .A »
m
Chgri dap an A
giiia hai dai l u o n g tren
„ ,
,
l a
= (0 = 27rf =^ f = _ : i ! B a x . . c h p n dap an A
A . 0,1s
m.w2
= coA
Cong suat tuc t h 6 i cua t r p n g luc P „ = P.v = m g v v o i v la van toe cua vat m .
= 27trad/s=>T = —= — = l s
VA2-X2
720^-10^
«
fir
271
V o i m va g la cae hang so nen P^sUax '^'^n\ax=
C h p n dap an B
V l d u 4 : M o t con lac 16 xo n a m ngang g o m vat nang tich d i f n q = 20|LIC va
PcsMax = mgVmax = ^ g A
16 xo CO do c u n g k = l O N / m . K h i vat dang n a m can bang, each d i ^ n , tren
— = g A ^ / k ^ (1)
=
J—A
Vm
Vm
mat ban nhan t h i xua't hien tuc t h o i m o t d i f n t r u a n g deu t r o n g k h o n g
Theo bai ra: nang m len den v j t r i 16 xo k h o n g bien d a n g r o i tha nh? nen
gian bao q u a n h c6 h u a n g dpe theo true 16 xo. Sau do eon lac dao d o n g
bien dp dao d p n g A = Al
tren m o t doan thang dai 4cm. D o Ion c u a n g d g d i ^ n t r u a n g E la:
^, m g
kA
D p bien d a n g cua 16 xo tai VTCB: Al = — = A = > m - —
A . 2.10^ V / m .
B. 2,5.10^ V / m .
^hdn
Thong thuang
C . 1,5.10^ V / m .
ir„ •;
..W ? j ; ,
D.lO^V/m.
tich vd huang ddn gidi
thi bdi todn eo liec la tdc dung vdo vat trong qud trlnh dao dong
Thay vao (1):
PcsMax = g A V k i ^ = ^^f'Y
^
^ 40.2,5.10-2 VlO.2,5.10-2 ^
thuang dugc xet vai con Idc dan. Tuy nhien a day bdi todn xet cho con lie Id xo nen
nhieu ban se xem day Id dang todn la vd thuang bo qua. Nhin chung thi cdc bdi
24
C h p n dap an C
25
Bi quyei on luy$n thi deii hqc dat diem tot da Vat li, tap 1-Le
Van Vinh
Fmax
V i dM 6 : (Trich de thi thu Quynh L i n i 1 - Ngh# An Ian 1 nam 2013)
Treo con \ic 16 xo tren tran cua mpt thang may, khi thang may dung yen thi chu
ky cua con lac la T, cho thang may chuyen dgng di xuong nhanh dan deu voi
gia toe a = 0,5g (g la gia toe roi ty do) theo phuong thang dung thi chu ky dao
dong dieu hoa cua no la T' va
A.T' =
2T.
B . T ' = T.
= 0,5T.
C.T'
D.T' = T V 2 .
^han tick Pd huang ddn gidi
A + Al
=^
76
= -
k
^
75
75
,„..
Chpn dap an B
Nhan xet: khi tim ra Al = 2,25(m) nhieu ban se boi roi vi qua Ion so vai cac dap
an decho. Cac ban nen binh tinh khai thdc gid thiet ticp theo ma tinh cho ra ddp so
Ndi chung Id hay binh tinh!
g' = g - a = g - 0 , 5 g = 0,5g
Al
Chu ky con lac thang may diing yen: T = 2n^ j—
=
(A + Al)
=^
sau do so sdnh vai ddp an. NeU c6 thi minh da diing con nen sai thi hay xem Iqi.
Xuong v i nhanh dan deu a i vi the F^, T nguoc voi P i suy ra
Chu ky con lac thang may chuyen dpng: T' = 2n^j^ = 2n / ^
k ( A + Al)
T h e o b a i r a : - ^ = -4^
V2T
V i the chpn dap an D
Ca B A I TAP V A N DUNG:
Cau 1 : (Trich de thi thu chuyen Hong Linh Ha tinh Ian 1 nam 2013)
Con 15c 16 xo c6 dp cung k va vat nho khoi lupng m c6 the dao dpng khong
ma sat tren mat phSng nghieng goe a so voi phuong ngang. 6 vi tri can
bang dp bien dang cua 16 xo la Al. Cho gia toe roi t u do tai do la g thi chu ky
dao dpng la
A.T = 2.pL:.
B.T = 2 . I ^ .
Ral tiec r^ng day khong phdi la dap an dung ma deym cau, vqy chung ta da sat lam tit
dau?. Rieng chu ky con lac Id xo thi chi phu thuoc vao dp cimg cua Id xo va khoi luang
am vat nqng ma khong phu thuoc vao vi tri dqt con lac nen khong phu thuoc vao gia toe C.T = 27:
D . T = 27i
trpng tru'ong. KJji thang may chuyen dong thi gia toe trpng tnecmg cua con lac sS la gia
^gsina
VAl
toe trong tntang hicu dung thay doi nhimg chu ki/ khong phu thuoc vao gia toe trong
d huang dan gidi
Thoi gian qua cau di tu vj tri cao nhat den vj tri thap nhat ehinh la di tu bien nay
qua bien kia mat — = 1,5 => T = 3(s).
Dp bien dang 16 xo tai VTCB: T = 27i
Vi the chpn C
Cau 2: (Trich de thi thu Nguyen Dinh Chieu - Tien Giang Ian 1 nam 2013)
Mpt con lac 16 xo, gom 16 xo nh^ c6 dp cung 50N/m, vat c6 khoi lupng 2kg,
dao dpng dieu hoa doc. Tai thoi diem vat co gia toe 75 cm/s^ thi no co van
toe 15^y3 (cm/s). Xac djnh bien dp.
A.A=6cm.
B. A=9em.
g
47t^
10.32
40
= 2,25(m)
D. A=10em.
(phdn tich ra huang ddn gidi
Tan so goe: (o =
gT^ _
C. A=5em.
=
= 5 rad / s
thiic dpc lap lien h^ giua van toe va gia toe:
v^
a'
'
a'
^
Luc dan hoi 6 vj tri thap nhat la lire dan hoi cue dai: F^g^ = k ( A + Al)
27
26
'Phdn tich v>d huang dan gidi
=> A =
= 6cm
20
= 10rad/s
0,2
He thuc dpc lap lien h? giiia van toe va gia toe:
Tan so goc: co = ^j— =
Chgn dap an A
Cau
2: (Chuyen Ha Tinh Ian 1 nam 2013)
(I) dieu ki^n kich thich ban dau de con lac dao dpng; (II) chieu dai day treo;
Chu ky dao dong nho ciia con lac dan phu thupc vao:
A. (II) va (IV).
B. (Ill) va (IV).
C. (II) va (V).
D. (I).
^hdn tkh v>d hu&ng dan gidi
Ta bie't rang: chu ky con lac dan dao dong dieu hoa phu thupc vao chieu dai
day treo va gia toe trong truong. Chpn dap an C
Cau 3: (Trich de thi thu chuyen Tran Phu Thanh Hoa Ian 1 nam 2013)
Mot con lac 16 xo thang dung 6 vj tri can bang 16 xo gian mot doan A/ . Neu
chieu dai 16 xo dupe cat ngan chi c6n bang 1/4 chieu dai ban dau thi chu ki
dao dpng ciia con lac 16 xo bay gi6 la
=
—+ •
(III) bien dp dao dong; (IV) khoi lugng vat nang; (V) gia toe trong truong,
•A=
10
v2
- ^
+
I (0
— 7 -
CO
co^A^
= 1
(200V3)
20^
10^
10^
= 4cm
:'<'• t o r
Chpn dap an D
Cau 5: (Trich de thi thii chuyen Ha Long Quang Tri Ian 1 nam 2013)
Con lie 16 xo CO khoi lupng vat nang la 85g dao dpng dieu hoa, trong 24s
thuc hi^n dupe 120 dao dpng toan phan. Lay
= 10. Dp cung ciia 16 xo ciia
con lac do la
y j
A. 85N/m.
B. lOON/m.
C. 120N/m.
D. l O N / m .
^hdn tich v>d huang dan gidi
Chu ky con lac 16 xo :
^
^hdn tick m hu&ng dan gidi
^
/m
At
4n^n^.m
k
n
At^
Gpi k va k' la dp cung ung voi 16 xo c6 chieu dai / va 1/4.
Dp cung va chieu dai 16 xo lien h^ qua cong thuc: kl = k'—=> k' = Ak
4
Dp gian ciia con lac 16 xo c6 chieu dai / tai VTCB:
- P « k A l = mg=>-^ = —
k
g
47t^l20^.0,085
• = 85N/m
24^
Chpn dap an A
Cau
6 (Trich de t h i dgii hpc nam 2013): Mot con lac 16 xo c6 khoi lupng vat
nho la m j = 300g dao dpng dieu h6a voi chu ki Is. Neu thay vat nho c6
khoi lupng mi bang vat nho co khoi lupng m2 thi con lac dao dpng voi chu
ki 0,5s. Gia tri m2 bang
A. lOOg
B. 150g
C.25g
D. 75 g
^hdn tich vd hu&ng dan gidi
Chu ky con lac 16 xo voi chieu dai //4:
Chu ky dao dpng cua con lac co khoi lupng mi va mi Ian lupt la:
Tj = 2n
Chpn dap an A
Cau 4: (Trich de thi thu chuyen Nhu Thanh Thanh Hoa Ian 1 nam 2013)
Mot con lac 16 xo c6 dp cung k = 20N/m, khoi lupng m = 0,2kg dao dpng
dieu h6a. Tai th6i diem t, van toe va gia toe eua vien bi Ian lupt la 20 cm/s va
2V3 m/s^. Bien dp dao dpng ciia vat nang la:
A. l O V S c m .
B. 16 cm.
C. 4 V 3 e m .
28
D. 4 cm.
mj _ Tj
2
m2 = nij.
1
[^2 J
= 300.
ro,5^
11J
= 75g
Chpn dap an D
CSu 7: (Chuyen Diic Thp Ha Tinh Ian 1 nam 2013)
Hai chat diem dao dpng dieu hoa dpc theo hai duang thang song song vai
tryc Ox, canh nhau, cung bien dp va tan so. V i tri can bang ciia chiing xem
29
n h u t r i i n g nhau (cung toa do). Biet rSng k h i d i ngang qua nhau, hai cha't d i e m
chuyen d o n g ngugc chieu nhau va deu c6 dp Ian l i do bang m p t nua bien dp.
H i e u pha cua hai dao d p n g nay c6 the la gia trj nao sau day:
C. 7i;
3
D.
271
^hdn tich ra hudrng ddn gidi
Theobaira:
=l i n . ^
=^
= 48cm
Dp bien dang ciia 16 xo tai VTCB:
1
(K^A\ — 1 ^ =
Al
4n^r
= 0,012m = 1,2cm
40.4,5^
. i^r;; v,';
Vay: IQ = l^b - ^1 = 48 - 1 , 2 = 46,8cm
V i hai vat dao d o n g dieu hoa ciing
•
,•
Chpn dap an D
bien d p va tan so nen ta bleu dien tren
cau
m o t v o n g tron n h u h i n h ve.
10: (Trich de thi thu chuyen Phiic Trach H a T i n h Ian 2 nam 2013)
Mot con lac 16 xo c6 k= lOON/m, dau tren co dinh c6n dau d u o i gan vat nang
H i e u pha ciia hai dao d p n g tren la — .
3
C h p n dap an D
i n = 0,4kg. Cho vat nang m dao dpng dieu h6a theo p h u o n g thang d i m g thi thay
thai gian 16 xo nen trong mpt chu k i la 0,1s. Cho g= 10 m/s^ «
m/s\n dp dao
dpng ciia vat la
Cau
A.8>/3cm
8: (Chuyen D u e T h p H a T i n h Ian 1 nam 2013)
B.4cm
L 6 xo nen
khi
A l < A . T h a i gian 16 xo nen k h i vat dao
d p n g tir
n g u a i ta thie't lap m o t dien t r u o n g nSm ngang, c6 h u a n g t r i i n g v a i true cua
- A l - > - A - > - A l (chieu d u a n g chpn thSng d u n g h u o n g x u o n g ) . V i the 16 xo
16 xo, CO c u o n g dp E = 8.10^V/m, k h i do vat d u n g yen 6 v j t r i can bang.
nen t r o n g m p t chu ky gap hai Ian t h o i gian vat d i tir - A l - > - A .
N g u o i ta d p t ngpt ngat dien t r u o n g . Sau k h i ngat dien t r u o n g vat dao d p n g
tn = 2 t ( _ ^ _ _ A ) = 0,1 => t ( _ ^ , ^ _ A ) = 0 , 0 5 ( 5 )
dieu hoa v o i bien dp bang
A . 12,5cm.
B. 2,5cm;
C. 4cm;
D . 2cm;
Goc vat qu^t d u p e t r o n g thai gian tren:
'Phdn tich m huang ddn gidi
cp = « . t ( _ „ _ A )
K h i CO dJQn t r u o n g vat d i r n g yen 6 v i t r i can bSng, k h i d o luc d i e n t r u o n g
can bang v o i luc dan hoi (phuc hoi). K h i d o t ngpt ngSt d i e n t r u o n g , vat se
bat dau dco d p n g dieu h6a v o i vj t r i bien dp la v j t r i vat can bang cu. Luc
cfo:
Fdt = F d h M a x «>
q E = k A =^ A =
qlE
k
-10
-6
.8.10^
40
= 0,02m = 2cm
C h p n dap an D
Cau
-Al
coscp =
-A
=^-.t(_^,_A)
Al
= — =>A
A
^
.0,05
Al
mg
=
=
cos
- Xem thêm -
d huong dan gidi
Dp gian cua 16 xo tai VTCB doi voi eon lac 16 xo dat nghieng mpt goc 37" so
A l o 2 = - ^ s i n ( a + Aa)
k
C a u 1 3 : Trong thang may treo mpt con lac 16 xo c6 do cung 25N/m, vat nang
CO khoi lugng 400 g. Khi thang may dung yen ta cho con IMc dao dong dieu
hoa, chieu dai con lac thay doi tu 32cm den 48cm. Tai thai diem ma vat 6 vj
tri tha'p nhat thi cho thang may di xuo'ng nhanh dan deu voi gia toe ^ = ^ •
Lay g = TC" = 10 m/s^. Bien dp dao dong ciia vat trong tru6ng hop nay la
B. 19,2 cm.
D. 5(rad/s).
"
.
Khi tang them goc nghieng 16° thi dp gian mai tai VTCB la:
5
Chpn dap an A
A. 17 cm.
C. 15(rad/s).
voi phuong ngang.
1 *i
•
A i mgsina
kAloi = m g s m a = > Aloi =
j^^
= 100
. =^T = 2 . / ^ = 2 . / l L = I s
Vk
37'' so voi phuong ngang. Tang goc nghieng them 16° thi khi can bang 16 xo
dpng rieng cua con lac la:
A. 12,5(rad/s)
B. 10(rad/s).
Cac lire tac dung vao vat tai vj tri can bang:
Fq, i+Pi
Viet
= 8cm
12,5cm. Chu ki dao dong rieng ciia con lac 16 xo la
B. 7t(s.)
D W H Khang