ThS. LE VAN
VINH
GIAO
VIEN
CHUYEN LUYEN THI DAI HOC
Bl
QUYET
ON
LUYEN
THI DAI HOC DAT
DIEM
TO'I
DA
VAT LI
TAP
1
THEO
TtfNG
onjYfiN
D6 vA
GiAi
an
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

Tong bien
tap : TS.
PHAM
THj TRAM
Bien
tap
Che
ban
Trinh
bay bia
THU
LUYEN
CONG
TY KHANG
VIET
CONG
TY KHANG
VIET
Tong phdt hdnh
vd dot tdc
lien
ket
xuat
ban:
CONG
TY TNHH MTV
DjCH
Vg VAN HOA KHANG VI|T
Dia ch?: 71 Dinh Tien Hoang
-

so
ISBN: 978-604-934-857-0
In
2.000 cuon,
kho
1
6x24
cm
- •
Tai:
Cty TNHH MTV IN AN MAI THjNH
DLfC
Dia chi: 71,
Kha Van
^an,
P.
Hiep Binh Chanh,
Q.
Thu
Dufc,
TP. Ho Chi
Minh
So
xuat
ban:
2033
-
201
3/CXB/03
-

cao
dang thi
sao! Co de
nhu tren khong?
Noi
chung
la
cung
khong
kho lam. The con
diem
10
trong
de
thi dai hoc thi sao!
Co
kho lam
khong?
Tai day
chac
nhieu
ban da c6 cau tra loi
roi!
Da
so
nhieu
ban cho
rang
dieu
nay

bo ich
truoc khi buoc
vao
phong
thi.
Cuon
sach
nay la
danh
cho cac ban
nhu
the
va
ciang danh
cho cac ban c6
nit.:-,i
tin
la
minh
se lam
duoc dieu mong
uoc do. Co so de
tin
vao
dieu
nay la
trong khuon
kho
cua
de

phiit).
Vay bi
quyet
nao
degiai
bai
toan
kho
khan
6
tren?
Bi
quyet
dau
tien
de c6
diem
10 la
phai bie't phan loai
cap do cau hoi va sau
do
de lam
truoc,
kho lam sau.
Bi
quyet
thu hai
la
phai
lam

giai quyet
cac bai tap
thugc dang
kho nay
cho nhanh
va
chinh
xac
nhat
la
nhiing
gi
cuon sach
lam
dugc.
Vi
the'de thuc
hien
dugc
bi
quyet thu hai thi
can lam
dugc nhiing
viec
sau:
1.
Su
dung thanh thao
moi
lien


dugc giai quyet true quan
de
hieu
va it ton
thoi gian (thi trac nghiem
can dieu
nay
nhat).
2. Phai
su
dung
tot
kien thuc
hinh
hgc
phang
de
tim
do
Ion cac dai
lugng
vecto.
Trong chuong
dao
dgng
co
thi
can nam va ap
dung dugc dinh

phuong
phap
vecto
trugt khong
the
khong bie't toi.
'
3. Sir
dung thanh thao
may
tinh
cam tay (Fx 570 ES
hoac
Fx 570 ES PLUS).
Trong
tinh
toan binh thuong
ma cac ban
khong
c6
thao
tac
nhanh tir
chie'c
ma>
tinh
thi
se mat kha
nhieu thoi gian.
Ngoai

sochpn
ban nay) thi cac ban
khong hgc cac kien thiic sau: nguyen chuang chuyen dpng cua vat ran, nguyen
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 tu anh
sang,
cac bai toan ve thay doi chieu dai, thoi gian trong thuye't tuong doi, cac
bai toan
giao
thoa anh
sang
bang cac dung cu quang hpc. Cac phan nay chi ra
ben ban nang cao vi the chiing ta phai loai bo ngay cac kien thiic nay de khong
bi
phan tam va mat thoi gian.
5. Nho
cong
thiic. Chiing ta khong the
diing

Le Van
Vinh
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.
Thuxingtti
ve:
Cty TNHH Mpt
thanh

2, Dao
dong
tudn
hodn
- 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
II.
PHl/ONG TRINH CUA DAO DONG
DIEU
HOA y
1.
Vtdu
- Gia su M chuyen dpng ngupc chieu
duong van toe goc la co, P la hinh chieu
ciia M len Ox. / cot -fj
Tai thoi diem t = 0, M co tpa dp goc (p
Sau thoi diem t, M co tpa dp goc
(ro.t
+
cp)
Khi
do: OP = x => diem P co phuong
trinh
la:
X
=
OMcos(cot
+

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)
4.
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.
III.
CHU KI, TAN SO, TAN SO GOC CUA DAO DQNG DIEU HOA
1.
Chu ki va tan so
Khi
vat tro ve vi
tri
cii,
huong cii thi ta noi vat thuc hi^n

- Van to'e eiing bie'n thien
theo
thoi gian
* Tai X = ±A thi v = 0
* Tai 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 THI CUA DAO DQNG 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.
VI.
CON LAC L6 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

KHAO SAT DAO DQNG CUAA LO XO VE MAT
NANG
LljQNG
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.
Nhan
xet
quan
trong:
dis'dat
diem
cao

DAO DONG
Bltu
H6K
I.
KHO
KHAN
KHI
GIAI
BAI TAP:
So lugng
cong
thuc yeu cau cac ban nho van dyng trong chuong dao dgng
CO
rat nhieu chi
tinh
phan to dam, bat
bugc
la 16
cong
thiic nhung voi so'
lugng
cac
cong
thuc do cung chi giai quye't dugc cac cau hoi rat co ban,
khong the giai quye't dugc he't cac dang bai tap dat ra cua chuong nay. O
phan dao dgng kie'n thuc toan lien quan la cac
cong
thuc lugng
giac
va giai

dang X = A
cos(cot
+
(Px),
de tim chu ki, tan so', duong di, khoang thoi gian
de di tu toa dg xi den toa do xi, tim van toe, gia toe tai mgt thoi diem nao
do,
khoang thoi gian 16 xo nen, gian
Tuy nhien se kho khan cho cac ban khi gap phai loai cau hoi dv! kien bai
toan khong cho phuong
trinh
dao dgng dang li do x =
Acos((ot
+
cp^)
ma
cho dang van toe tue thai v
=-A(osin(cot
+ (Px)hoac cho dang gia toe tiic
thoi
a =
-(a'^Acos((ot
+
(Px)
•
Luc nay hau he't cac ban deu bi dgng khong the
bieu dien ham (v) va ham (a) tren duong tron lugng
giac.
Muon
bieu dien dugc tren duong tron lugng

thuc, cac moi quan he phuc tap cua cac
dai
lugng co hge, vi thie'u
tinh
true quan, thie'u moi quan h^ gSn bo giira cac
hi^n
tugng vat ly nen thuong tra loi sai cac cau hoi du co ban nha't.
6
Sau
day la phuong phap
khac
rat tryc quan, the hien dugc mo'i quan he
giira
cac dai lugng nham
giiip
cac ban trong
vi#c
giai nhanh nha't, chinh xac
nha't cac dang toan ve dao dong co,
song
co, dong dien
xoay
chieu va dao
dgng trong mach LC. co the noi rang: phuong phap
diing
duong tron lugng
giac
quye't
dinh
Ion den

ngugc
chieu true sin nen co chieu (+) huong tir tren xuo'ng voi bien dg
v^ax^^-'^-
Dieu nay tuong duong voi ham v =
Acocos(cot
+
(Pv)
voi
+ Gia toe tuc
thoi:
a = -a)^Aeos((ot +
cpx)
la ham
trir
cosin
(ngugc
ham x)
=>
ngugc
chieu true cos co huong (+) tir phai
sang
trai
voi bien do a^^
=cf^A
Dieu nay tuong duong voi ham: a =
a)^Aeos(cot
+
(Pa)
voi (pg =
(p^,

cue dai, dgng nang cue tieu
- Vi tri can
bang
II:
(x=0; v = -coA; a=0)
=>
The'nang
cue tieu, dong nang eye dai
Vi
tri bien am III:
(x = -A; v=0; a^^^x
=co^A)
=> Thenang cue dai, dong nang cue tieu
- Vj tri can biing IV: (x=0;
v^-,^=wA;
a = 0)
=> Tlie'nang cue tieu, dong nang cue dai
Kei
luan:
Vay dm ki dao dgn^
titan
hoan
cua ham dgn^
nang
va ham
thenang
cua
dao
dong
dieu

Vung
2: (x < 0; v < 0; a > 0)
=> vat chuyen dong cham dan
theo
chieu (-) vi
a.v<0
va the nang tang,
dong nang giam.
Vung
3: (x <0; v > 0; a > 0)
=> vat chuyen dong nhanh dan
theo
chieu (+) vi a.v >0 va the nang giam,
dong nang tang.
Vung
4: (x>0; v>0; a < 0)
=> vat chuyen dong cham dan
theo
chieu (+) vi
a.v<0
va the nang tang,
dong nang giam.
+ Mo'i
quan
he
vepha
eua li do (x), van toe
(v),gia
toe (a): Qua hinh ve nhan
tha'y dugc moi quan he ve pha ciia ham li do (x), van toe (v) va gia toe (a) la:

van
toe ciia vat tai thoi diem t = 7,5s la:
A.
V =
Ocm/s.
B. v =
75,4cm/s.
t\. ;
C. V =
-75,4cm/s.
D. v =
6cm/s.
^hdn
tich
vd
huong
ddn
gidi
Dung
true Ox bieu dien :
lue ban dau vat 6 vj tri I sau thoi gian
t
= 7,5s vat quay mot goc:
cot =
271.7,5
= 1571 lap lai 7,5 vong a
den vi tri III => co van toe v = 0.
Chpn
dap an A
II

cos c6 dang: x =
6cos(47it)
cm
=> ban dau vat 6 vj tri I sau thoi gian
t
= 5s vat quay 1 goc o)t - 4n.5 - 20n
lap lai 10 vong den vj tri cij.
=> CO gia toe a = -co^A =
-947,5^
s
Chgn dap an C
Vl du 3: Mot
chat
diem dao dong dieu hoa
theo
t c6 phuong
trinh
van toe
v
=
107reos
27rt + - em/s, toa dp ciia
chat
diem tai thoi diem t = 1,5s la
V 2 J
_A.
x = l,5cm. B. x = -5em. C. x= + 5cm. D. x = 0cm.
9
'Phdn
tich

theo
chieu duong cua true tpa dp.
A.8/3S
B.2/3S
C. 2s D. 4/3s
^hdn tkh vd
hii&ng
dan
gidi
Bien do A = ^^ = —= 4cm
CO
0,5Tt
Dung
tryc Ov bieu dien:
Luc ban dau vat 6 vi tri V
(POv =-7
o
^Ov
=
sau thai gian t vat quay 1 goc
a = cot =
0,57rt
=
—
vi c6 li dp x = 2cm,
3
bien dp A = 4 cm va chuyendong
theo
chieu {+) den vj tri VI
=> mat thoi gian t = 2/3s. Chgn dap an B

DWH
JOtang
Vift
Bl/ofC 3: Bieu dien dao dpng dieu hoa tren duong tron. Vat di tir vi tri Xj
den X2 tuong ung voi mpt chuyen dpng tron deu di tir M deh N vai van
toe goc
CO,
ban
kinh
la A. «,
Slide
4: Xac
djnh
goc
cp
=
MON.
. .,;.
=> Thai gian vat di tu vi tri Xj den X2 la : At = —.
CO
m vi DU MAU:
Vi du 1: Vat dao dpng dieu hoa voi phuong
trinh
x =
Acos(cot
+ cp) (cm).
Tinh
thai gian ngan nhat vat di tu:
A
a) Vj tri can

Acp 6 T
VTCB
deh X = - la: At =
2 CO
27t 12
T
b) Khi vat di tir vi tri can
bang
den
AV2
^ ,
-, tuong ung vol vat chuyen
<l9ng
tren duong tron tu M deh N ^
dupe mpt goc Acp nhu hinh ve ben.
De thay: sin
Acp
= — => Acp = - rad.
2 4
^ V I—
=i> Khoang thoi gian ngan nhat de vat di tu
VTCB
deh x = —— la:
Bi
qtiyei
on
luyen
thi dai hoc dat
diem
toi da Vat It, tap l~Le Van

n
_3_
2n
T
I
6
d) Khi vat di tu vi tri can bang den x =
tuong
ung vcVi vat chuyen dong tren
duong
tron tu M den N duoc mot goc
Acp
nhu hinh ve ben.
De thay: sin
Acp
= ^ =>
Acp
= ^ rad.
=> Khoang thoi gian ngan nhat de
vat di tu VTCB den x = A la:
Acp
2 _^
At
=
-
CO
Tom lai: ta c6 bang thoi gian trong dao dong dieu hoa sau:
-A
o
T_

nlid't
neii
dccho
diem
di va
diem
den dqc
bict
nhu
tren.
p
BAI TAP VAN
DUNG:
CaU
1: Vat dao dong dieu hoa voi phuong
trinh
x =
Acos(cot
+ cp) (cm). Tinh:
a) Thoi gian ngan nhat vat di tu vi tri c6 li do
X|
= den vi tri c6 li do
A
• •
X2
=
A
b) Thoi gian ngan nhat vat di tif vi tri c6 li do ^\ — den vi tri c6 li dc)
A
' 2 •

( A
2
2
= t
Asfd.
>0
+ t,
0-^
2
;
=
1 L-1
~ 6^ 4
Ta bieu dien cac diem tren len true dao dong dieu hoa se thay ro hon
~A
_AS
A42 _A
A Ayll A41
o
\
T
•1 ^
]
12
r * '
4
1
-x
Bf quyei on liiyen ilii dai hoc dat diem tot da Vat It, t^p 1-Le Van Vitth
b) Khoang thoi gian ngan nha't vat di

A>/2
AV3
xi = — den X2 =-y-
theo chieu am tuong ung voi vat chuyen
dong tren duong tron tu M den N.
A>/2 A73 1
2 -
= t
+
t(O^A)
+ t
=
1 I
fl_ll
IIT
12
Bieu dien len true dao dong dieu hoa
^V3 A42 A
-A
O
A
2
A-Jl
T
8
T T
6 4
Thai gian dao dong cua vat dugc xdc dinh nhu a tren nhimg hinh ve duai eho edc
ban
CO

toan
xac
djnh
thdi
diem
vat di qua vj tri x da
biet
(ho$c
V, a, \Nt, Wd, F) Ian thuT N
PHl/QNG
PHAP
* 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 dua vao x (hoac v, a, Wi,
WJ,
F)
A(p
Ap dung 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 thu N. ^
Cdc loai thucmggap vd cong thiic tinh nhanh
- Qua
X

ban dau)
-
Qua X ke den
chieu
(+ ho|c -)
t
= (N - 1)T + tj (ti
thoi
gian
de vat di qua vi
tri
x theo
chieu
dau bai quy
dinh
Ian
thii
1 ke tu
thai
diem
ban dau)
m
vi DU MAU:
VI
dy 1: Mpt vat dao
dong
dieu
hoa voi
phuang
trinh

V
=
-167tsin
47rt+-
6
=2
7l^
47rt+-
6J
>0
=>47tt+-
= — + k27t
6 3
=>t = -— +
—
keN .
Thoi
diem
thu
3
line
voi k = 3=> t = —s
8 2 ^8
Cach
2: Su d\ing duong tron
luQmg
giac
Pha ban dau
(p
=

quet
A(p
= 2.2n +
3n
t=^=Hs
CO
8
Hoac
tinh
theo cac
khoang
thoi
gian
dat
biet:
4V3
AV3 . o 4 A
XMO
=^ = -r-va XM2 =2 =
-A
t
Mo^M2
-VA /3
2 2
(O^-A)
+ '(-A^O)
+
t
Mo
f

di
qua
vat
Id
rdi
l&n
thi
ta
lam nhu vi du sau
Vl
dM 2: Mpt vat dao
dpng
dieu
hoa voi
phuong
trinh
x =
4cos(47tt
+
—
)cm.
6
Thoi
diem
thu
2013 vat qua vi
tri
x = 2cm.
12073
^-

dong:
T = — = — = - (s)
CO 47t 2
x
= 2
47tt
+
—
= - + k27:
6 3
47ct
+ - = — + k27t
6 3
t
= A +
ii
(keN)
24 2 ^ '
t
= -i + Ji
(keN*)
8 2^ '
N-1
T
+
ti
Thoi
diem
thu
2013 (le) nen ta

Vat
qua vj
tri
x = 2cm Ian
thu
2013 la :
t =
N-1
^
^ 2013-1 1 1
12073
T
+
ti
= + — =
2 " 2 2^24 24
Chpn
dap an A
Cach
2: Su dvng duong tron
lupng
giac
Vat
qua x = 2 la qua Mi va
M2.
-A
Vat
quay
1
vong

.2
-^0
Tjr __T
6 12~12
T 0 5
12073
^ t =
1006T+
— =
1006.0,5+
—
=-^=^s
12 12 24
m
BAI
TAP VAN
DUNG:
Cau
1: Mpt vat dao dong dieu hoa vai x =
8cos(27it
- —) cm. Thai diem
thii
6
2012 vat qua vj tri c6 v = -87t cm/s.
A.
1005,5s
B.
1005s
C. 2012 s
'Phdn

= l.k
2
keN
N-2,
Vat qua Ian thu 2012
(chan)
nen ta dung cong thuc : t = —^—T +12
Voi
la thoi gian de vat di qua vj tri x = 2cm Ian
thii
2 ke tu thoi diem ban
dau ung vai k = 0 (nghiem duai).
Vay
t. =i + k = - + 0-i(s)
•y 2 ^ 2 2^ ^
Vat qua vi tri x = 2cm Ian thu 2012 la :
^ N-2„ ^
2012-2,
1
t
= T + t, = .1 + - =
1005,5
(s)
2 ^ 2 2 ^ '
Vay chpn dap an A
Cach 2: Su diing
duang
tron
lug^ng
giac

tri
vat di qua la N va P.
Pha ban dau
cp
= - — => ban dau vat 6 M.
6
Vat qua vj tri can tim Ian thu 2 tai P khi do
T
vat quay duoc nua vong nen mat ^2
Qua Ian thu 2012:
t
= ^^Y^T +12
=
^^^I^T
+1
=
1005,5T
=
1005,5(s)
Nhan xet: a day ta
hieu
dien
duang
tron
theo
v
detinh
nhanh
han.
Cau

2
27rt-^
1
2*2 2
= -mo) A cos
2nt-
n
I
3^
2
3.
o sm
2nt-^
3
= cos
2nt-^
3
1-cos
47tt
3
1
+ cos
47tt-
271^
cos
47tt-
2n^
A
. . 27t 7t , ^ 7 k
=

diem
tot da Vat It, tap 1 - Le Van Vinh
Cach 2: Su dung duong
tron
lugng
giac
A
Wd
= W.
x=±
72
•
CO
4 vi
tri
Mi,
M2,
Ma,
M4
tren duang
tron.
Pha ban dau
cp
= — nen ban dau vat a Mo
3
Thoi
diem dau tien vat qua vi
tri
Wd
=

= 3Wt ^ sin
2.t-^
= ^
2 3
2,tt-^
= -^ + k2K
=
3cos^
4
>cos
1
"2
k27i
t
= —+ k keN
12
t
= - —+ k keN
12
Qua
Ian thu 2010 (chin): t =
N-2
T + t, =
2010-2
„ 11
12059
2 + — =
.
12
12

.3
4) 12
=>t
=
^ =
1004.11
= l^s
CO
12 12
A(p
=^
502.271
+
71
-
20
D?ng 4. Xac
dinh
so Ian vat di qua x trong
thcfi
gian
tu"
ti den
tz
(At = t2 - ti)
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 di qua 1 Ian
* Xac

la so ian di qua x khi tren vong trong
lupng
giac
quay dupe goc
0,p.27t
ke
tir
vi
tri
ban dau
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 tu vj
tri
ban dau
m vi DU MAU:
Vi
du 1: Cho vat dao dpng dieu hoa theo phuong
trinh:
X
=
3cos
47rt-^
3,

1,2s dau tien tuc:
1
k
t = -+- (keZ)
6 2^
t = l (leZ)
21
Bi(juyei
on
luyen
thi
itai
hoc
itat
dicin
tot da Vat li,
i,ij>
I - Le V&ti
Vitth
0<t
<1,2<=>
0<i + ii<l,2
6 2
0<-<l,2
2
-0,33<k<2,07
0<1<2,4
k
= 0;l;2
1

Goc ma vat
quet
dugc
trong 0,2s la:
BOM =
A(p
= co.At = 47t.0,2 = 0,
Snrad
Goc ma v|t
quet
dupe tu A den B la:
AOB = —rad.
, 3
So
sanh
hai gia trj tren
Ta c6: BOM > AOB => vat di qua A
=^N' =
1
+
1
= 2 ii> N = 2.2 + 2 = 6.
Vay CO 6 Ian vat di qua vj
tri
c6 li dp 1,5 cm
22
CtyTNHIt
\
/ I nWH
Kham;

+
CO CO
Chieu dai quy dao: S = 2A
m vi DU MAU:
Vi
du 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

23
Vl
du 2:
(Trich
de thi thu Nam
Tr^c
- Nam Dinh Ian 1 nam 2013)
Mpt
vat dao dong dieu hoa voi gia toe cue dai amax va toe dp c^c dai
Vmax.
Tan so dao dong la
£
_ ^max g £ _ ^max Q f _ ^^-^max -Q
£
_ ^max
^hdn
(icfi
pd huang ddn gidi
Bdi
nay dan gidn chi Id tim moi lien he giua gia toe cue dai vd toe do cue dai.
Gia
toe cue dai: a^^^ = co^A
Toe dQ cue dai: v^^^
=
coA
Tu
day ta lap ti le la eo ngay
lien
giiia
hai dai luong tren

Khi
do dai vat la lOcm nen li dp x =
±10cm
De cho quy dao dai S = 2A = 40 ^ A = 20cm
Ap
dung he thuc doc lap
lien
he
giira
li do va van toe
•
+ - = 1=>C0 =
-
207t73
=
27trad/s=>T
= —= —= ls
A'
(coAf
VA2-X2
720^-10^ « 271
Chpn
dap an B
Vl
du 4: Mot con lac 16 xo nam
ngang
gom vat
nang
tich
difn

^hdn tich vd huang ddn gidi
Thong
thuang thi bdi todn eo
liec
la tdc dung vdo vat trong qud trlnh dao dong
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
todn ve'luc, each gidi chung
nhat
Id tim hap luc tdc dung vdo vat gay ra gia toe
chuyen dong cho vat.
Cach
giai bai nay nhu sau:
Con lac dao dpng tren doan thang dai 4cm chinh la quy dao chuyen dpng
ciia
vat S = 2A = 4cm, vi the bien dp dao dong cua vat la A = 2cm.
Khi
vat m dao dong, hop luc cua luc di?n truong va luc dan hoi gay gia toe
a cho vat.
Tai vi tri
bien,
vat c6 gia toe cue dai. Khi do ta c6:
Fd
-
Fdh
=
m.amax
qE - kA = m.w2 A = m. — .A » qE = 2kA =i> E = 2.10^ V/m
m

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.
Trong
dao dong dieu hoa, van toe chuyen dong cua vat Id van toe tiec thai nen eong
suat
ciia
luc cung Id eong suat tiec thai.
Sau
day la each giai cu the bai
toan
nay:
Cong
suat
tuc
th6i
cua trpng luc P„ = P.v = mgv voi v la van toe cua vat m.
fir
Voi
m va g la cae
hang
so nen P^sUax '^'^n\ax= =
J—A
V

PcsMax
=
gAVki^
= ^^f'Y ^ ^ 40.2,5.10-2
VlO.2,5.10-2
^
Chpn
dap an C
25
Bi
quyei
on
luy$n
thi
deii
hqc dat
diem
tot da Vat li, tap 1-Le Van
Vinh
Vi
dM 6: (Trich de thi thu Quynh
Lini
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

T' = 2n^j^ = 2n / ^
= V2T
Vi
the chpn dap an D
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

chu ki/
khong
phu
thuoc
vao gia toe
trong
tnfcmg
nen chu ky con idc vi
the'ding
khong
doi.
Dap an B
m&i
la dap an
dung.
ChgnB
Vi du 7: (Trich de thi thu Quynh
Lini
1 - Nghf An Ian 1 nam 2013)
Mot
con lie 16 xo treo thSng
diing
dupe kich thich eho dao dpng dieu hoa.
Th6i
gian qua cau di tir vj
tri
cao nhat deh vj
tri
thap nhat la 1,5s va ti so'giua
dp

—
= 1,5 => T = 3(s).
Dp
bien dang 16 xo tai VTCB: T =
27i
gT^ _ 10.32
=
2,25(m)
g
47t^ 40
Luc dan hoi 6 vj
tri
thap nhat la
lire
dan hoi cue dai:
F^g^
= k(A + Al)
26
Fmax
k(A + Al) (A + Al) A + Al 76
Theobaira:-^ = -4^ = ^ = ^ = -
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

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 tu do tai do la g thi chu ky
dao dpng la
A.T
=
2.pL:.
B.T
=
2.I^.
C.T = 27: D.T = 27i
^gsina VAl
<Phdn
tich
ra
huang
ddn
gidi
Chu
ky eon 15c 16 xo dao dpng dieu hoa tren mat phing nghieng goe a so
voi
phuong ngang: T =
27t
J— = 2n
k
ygsina
Vi
the chpn C

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;
(III)
bien dp dao dong; (IV)
khoi
lugng vat nang; (V) gia toe trong truong,
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
^hdn
tick
m
hu&ng
dan

2V3 m/s^. Bien dp dao dpng ciia vat nang la:
A.
lOVScm. B. 16 cm. C. 4V3em. D. 4 cm.
28
'Phdn
tich
v>d
huang
dan
gidi
Tan so goc:
co
= ^j— =
20
0,2
=
10rad/s
He thuc dpc lap lien h? giiia van toe va gia toe:
—+
•
= 10
co^A^
= 1
•
A =
v2
-^ + —7-
20^
10^
(200V3)

= 85N/m
At^
24^
Chpn
dap an A
Cau 6 (Trich de thi
dgii
hpc nam
2013):
Mot con lac 16 xo c6
khoi
lupng vat
nho la mj =
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

triing
nhau (cung toa do). Biet rSng khi di ngang qua nhau, hai
cha't
diem
chuyen dong ngugc chieu nhau va deu c6 dp Ian li do bang mpt nua bien dp.
Hieu
pha cua hai dao dpng nay c6 the la gia trj nao sau day:
3
C. 7i;
D.
271
^hdn tich ra
hudrng
ddn
gidi
Vi
hai vat dao dong dieu hoa ciing
bien dp va tan so nen ta bleu dien tren
mot
vong
tron
nhu
hinh
ve.
Hieu
pha ciia hai dao dpng tren la — .
3
Chpn
dap an D
Cau 8: (Chuyen Due Thp Ha Tinh Ian 1 nam 2013)

dJQn truong vat
dirng
yen 6 vi tri can
bSng,
khi do luc dien truong
can bang voi luc dan hoi (phuc hoi). Khi dot ngpt
ngSt
dien truong, vat se
bat dau dco dpng dieu h6a voi vj tri bien dp la vj tri vat can bang cu. Luc
cfo: Fdt =
FdhMax
«> q E = kA =^ A =
qlE
-10
-6
.8.10^
=
0,02m
= 2cm
k
40
Chpn
dap an D
Cau 9: (Trich de thi
thtr
chuyen
VInh
Phuc Ian 1 nam 2013)
Mot
con lac 16 xo trco thang diirng va dao dpng dieu hoa voi tan so'

= 1,2cm
Al
4n^r
40.4,5^
.
i^r;;
v,';
Vay:
IQ
= l^b - ^1 = 48 -1,2 =
46,8cm
• , •
Chpn
dap an D
cau 10: (Trich de thi thu chuyen Phiic Trach Ha Tinh Ian 2 nam 2013)
Mot
con lac 16 xo c6 k= lOON/m, dau tren co
dinh
c6n dau
duoi
gan vat nang
in
= 0,4kg. Cho vat nang m dao dpng dieu h6a theo phuong thang
dimg
thi thay
thai
gian 16 xo nen trong mpt chu ki la 0,1s. Cho g= 10 m/s^ « m/s\n dp dao
dpng
ciia vat la
A.8>/3cm

kcoscp
V2 100
• 2
Chpn
dap an C
Cau 11: (Trich de thi thu chuyen Thi|u Hoa Thanh Hoa Ian 2 nam 2013)
Con lac 16 xo dat tren mat phSng nghieng goc a khong ma sat thi chu ki dao
dpng
rieng ciia con lac phu thupc vao
A.
goc a va dp cirng 16 xo.
B. goc a, khol lupng vat va dp cung 16 xo. *' *• ''
1.
kho'i
lupng cua vat va dp cung 16 xo. <
•
«
).
goc a va
kho'i
lupng ciia vat. '
^hdn tich vd
hu&ng
ddn
gidi
Ihxi
ky con lac 16 xo dao dpng dieu h6a tren mat phang nghieng goc a so
/oi
phuong ngang: T =
27i./—

luang
ma con phu
thuoc
vao goc a, gia toe g va do
bien
dang
cua Id xo tai VTCB AI.
Chac
c6 le so
litong
kel
luqn
dieu
nay se
khong
it
dung
khong
cdc ban! Tuy
nhien
kei
luan
the
nay la sai ban
chat
nghiem
trong
day.
Theo
nhu

chinh
xdc nhe! Dap
an
cudi
cimg
Id C vi Id xo cd dat
trong
tu the ndo thi chu ky cua no van chi phu
thuoc
vao do
cimg
cua Id xo va
khoi
Iwgng
cua vat
nqng
thoi.
Chpn
dap an C
Cau
12:
(Trich de thi thu chuyen Nguyen Thi Minh Khai - Ha tinh Ian 1
nam 2013)
Mot
con lac 16 xo treo thang dung trong thang may. Khi thang may di len
nhanh dan deu voi gia toe a = g / 4 thi tai vi tri can bang 16 xo bj dan doan
12,5cm.
Chu ki dao dong rieng ciia con lac 16 xo la
A. |(s). B. 7t(s.)
C.2(s).

=
2./^
=
2./lL=Is
Vk VlOO 5
Chpn
dap an A
Cau
13:
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
A.
17 cm. B. 19,2 cm. C. 8,5 cm. D. 9,6 cm.
32
Cty TNHH MTV DWH Khang Viet
<Phdn
tich

0,016m
= l,6em
k
25 ,fi, ;
Vay sau do vat dao dpng bien dp:A' = A + x = 8 + l,6 =
9,6cm
Chpn
dap an D
Cau
14:
Mot eon lac 16 xo dang can bang tren mat phSng nghieng mpt goc
37'' so voi phuong ngang. Tang goc nghieng them 16° thi khi can bang 16 xo
dai
them 2cm. Bo qua ma sat, lay g «10m/s^ ; sin 37" * 0,6. Tan so goc dao
dpng
rieng cua con lac la:
A.
12,5(rad/s)
B.
10(rad/s).
C.
15(rad/s).
D. 5(rad/s).
<Phdn
tich
v>d
huong
dan
gidi
Dp

. Chpn dap an B
m
33
Bt
iiuifet
on liiin'ii thi diii hoc 4at
diem
tot da Vat li, tap 1 - Li Van
Vinh
Chuydn de 3
QUANG
BUdNG
- TdC
fiO
TRUNG
BINH - V^N TdC
TRUNG
BINH
CAC
DANG
TOAN
VE
QUANG
Dl/QNG
D^ng 1. Quang dUdng vat di dUcrc uTng vdi khoang
thdi
gian
dac bi^t
+ Quang duong di trong 1 chu ky luon la 4A; trong 1/2 chu ky luon la 2A
+ Quang duong di trong 1/4 chu ky khi vat di tu

^han
tick
m
huang
dan
gidi
Bai
todn
khong
cho
thai
diem
ban dau ti vat d dau, vi
theneu
ti le
thai
gian
khong
ndm
trong
truang
hap dac Met thi bdi
todn
se di vdo be tat. Do do ta can xdc
dinh
ti
sotren
c6 gid tri
nguyen
hoac

= t2 - ti
Tu duy
loai
nay:
trong
thai
gian
T/2 (goc
quay
tren
vdng
trbn
la: n) vat
dddh
se di
duoc
quang
duang
la lA. Ta de xdc
dinh
quang
duong
di
duoc
neu
thai
gian
Id nho han T/2 (goc
quay
nho han n) dua vdo

S2
+ Trong do Si la quang duang vat di
duoc
trong n.T (chu ky) hay
Si
= n.4A va
S2
la quang duong vat di
dugc
trong thoi gian 0,pT .
De xac
dinh
S2
ta xac
dinh
goc quet
cp
tren vong tron
(p
= co.O, pT tu do suy
ra
S2.
T
Cach
2:
Tach
At theo -
- lap ti so: ^ = n,p- n + 0,pvoi n = 0; 1; 2
T T
-

se quay goc nn + 0,pn)
- khi quay goc nn vat di
duoc
quang duang Sj = n.2A
- khi quay goc A(p = 7r.0,p tu vi tri ban dau (xi, vi) ta dua vao vong trgn
lugng
giac
ta tim dugc quang duang di la $2
- vay quang duang vat di dugc la S
= Sj +
S2
= n.2A +
S2
DU MAU:
VI
du 2:
(Trich
dethi
thtt
chuyen
Trdn
Phu -
Thanh
Hoa Idn 1 nam
2013):
Mgt
con 13c 16 xo gom mgt vat nang m = lOOg mac voi 16 xo c6 dg cung
k
=
160(N/m)

Theo bai ra: t = 0
liic
vat di qua VTCB theo chieu duong chinh la diem Mo
Tan
so goc: =,/— = = 40
rad
/ s
™ , , „ 271 27t 71
Chu
ky: T = —
=
—
=
—s
^ CO 40 20
Cach 1: Tach At theo T
Ta
lap ti so'
giiia
khoang
thoi
gian de
cho voi chu ky dao dpng cua vat:
t
6,4
=
3,125
20
Tie
do ta phan

Cach 2: Tach At theo -
2
Ta
lap
ti
so
giira
khoang
thoi
gian de cho vai nua chu ky dao dpng cua vat:
7t
4^
=-^ = 6,25 = 6 + 0,25
1
71
T
T
At
= 6-+ 0,25-
2 2
2 2.20
Vgy quang duang vat di la S = Sj + = n.2A +
82=
6.2A +
S2
T
S2
la quang duong vat di dupe
trong
khoang

Vay S
=
Si
+
S2
= 143,8(cm)
Cach 3:
tim
ngay goc quay
Ta
lap
ti
so'giiia goc quay dupe
trong
khoang
thoi
gian de cho voi
7t:
40.^'^
A(p^o)At^__M ^6,25 = 6 + 0,25 ^ A(p =
67t
+
0,25.7i
'i
n
n n
Vay quang duong vat di la S
= Sj +
S2
= 6.2A +

=
-
t2-ti
vdi
S la quang dUdng
tinh
nhu"
tren.
m VI DU MAU:
Vi du 3: Mot vat dao dpng dieu hoa theo phuong
trinh
x
=
6cos
7rt +
^
4
(cm).
Trong
khoang
thai
gian ngan nhat
khi
vat di tu vi
tri
c6
li
dp x = -3 cm
den vi
tri

r
: 8
•
]
.—T
;
37
Btquyei
dn luyfti thi d^i hqc dat
diem
tot da Vgt It, tap 1-Le Van Vitth
\f3 A
Thai gian ngan nhat vat di tu vj tri x =
"A —
den vi tri = - y la:
AN/3
A
2
= t
(-
Ax/3
T T T 2 1 ^
2 .0) (-y-»0) 6 12 12 12 6
Quang duong tuong ung trong thoi gian tren la:
S =
AV3
A
2 ^2^
JV^-1)A^(V3_1)6^3^^_^^
Toe dp trung binh trong khoang thoi gian tren la:

A.
16cm/s
B.
32cm/s
C. 64 cm/s D.
96cm/s
'Pkdn
tick
pd
hu&ng
dan
gidi
Theo
bai ra, ta c6: P la trung diem ciia OM va Q la trung diem cua ON,
-A
O
L
12
T
L
12
S = A
Xp =
OM
A
ON
2 =y''Q=""2
Quang duong vat di dug-c: S =
|xp
-

s
Chpn dap an D
'^^i^S.
Bai toan tinh
quang
dUdng I6n nhat va nho nhat vat
di du'^c trong khoang thdi
gian
0 < At < T/2.
Hinh
1
Hinh
2
Vgt
CO
van toe Ion nha't khi qua VTCB, nho nha't khi qua vi tri bien nen
trong
cung mot khoang thoi gian quang duong di dupe
cang
Ion khi vat
6
cang
gan
VTCB
va
cang
nho khi
cang
gan vj
tri

T
+ Trong thoi gian ny quang duong luon la 2nA
Trong thoi gian At' thi quang duong Ion nha't (nho nhat)
tinh
nh^ftren.
"' ' 39
m JjUyH
AH
Itliffti tht dat
Hp?
,Ii:„, t.n ,la Vat It, iapi-Le V3n Vinfr
S„a^
=n2A + 2Asin^ = n2A + 2Asin^
Smin
=n2A + 2A
Acp'
1
-
cos—^
' coAt'^
1
- cos
= n2A + 2A
V
— y
+ Toe
CJQ
trung
binh
Ion nhat va nho nhat ciia trong khoang thai gian At:

gidi
a. Goe ma vat quet dupe trong
thoi
gian — la:
A(p
= co.At = —— = -
6 T 6 3
Ap
dung cong thuc
tinh
S
min
t3
CO'.
l-cos^
=2A
-A
2 2 2
1
-
cos—
6
O
=
A(2-V3)
2 2
—• r-
S
,.,.,=2A
3

Ayfl A^
T
8
I
8
S
2T T T T
c. DoAt = —
>-=>At
= - + -
3 2 2 6
Quang duang ma vat di dupe trong —
luon
la 2A.
2T
Quang duong nho nhat ma vat di dupe trong — chinh la quang duang
3
T
nho nhat ma vat di dupe trong —.
6
T
Theo
eau a ta tim dupe quang duong nho nhat ma vat di dupe trong — la
6
A(2-N/3).
Vay quangi
S^i„=2A
+ A(2-V3) = A(4-V3)
2T
Vay quang duang nho nha't ma vat di dupe trong — la:

nen luc dan hoi chinh la life hoi
phuc.
Dehai
CO
de cap den luc keo cua Id xo, ma luc keo cua 16 xo
chinh
la luc dan hoi vi the
ciingla luc hoi
phuc.
Theo
bai ra, ta co h$ phuong
trinh
sau:
^kA2=l
kA
= 10
>A = 20 em.
41
Thoi
gian ng§n nhat
lien
tie'p de
Fhp
= — Fhpm« la - = 0,1 =>T = 0,6s
2 6
. At 0,4 4 1
. Thmg.an^ = -^ = - = l + -
2 "2
„ IT T T
=> At = — + — = — +—

la S = 2A
+ Quang duong Ian nhat di dugc: S^^g^ = ^ +
Sj^^ax
= 2A + A = 3A =
60cm
Chpn
dap an B
Vl
diJ 7: (Trich
Aethi
thit
truang
chuyen
Lam Son
Thanh
Hoa Idn 2 nam
2013):
Mpt
vat dao dong dieu hoa voi bien do A va chu ki T. Toe do
trung
binh
3T
Ion
nhat ma vat di dugc trong
thoi
gian — la
4
^
A(8
+ 4>/2) g

nhat ma vat di duoc trong —.
4
42
^ Cty TNHH MTV DWH Khang Vie
I
Goc ma vat quet dugc trong
thoi
gian - la:
A(p
= co.At = — - = -
T
Quang duong Ion nhat ma vat di dugc trong — la:
Simax =2Asin4r = 2A sin ^ = AN/2 "''
-'Imax 2 4
3T
V^y
quang duong Ion nhat ma vat di dugc trong — la:
S„ax=2A
+
AV2=A(2
+ V2)
Toe dg
trung
binh
Ion nhat ma vat di dugc trong
thoi
gian — la: ;
S _ A(2 + >/2)^ A(8 + 4N/2)
|VTBmax
- - 37 - 3-^

todn
xudi
cho tot
m Vi DU MAU:
Vi
du 8: (Trich
dethi
thit
truang
chuyen
Ha Tinh Idn 1 nam
2013):
Vat
dao dgng voi phuong
trinh
x = 4cos(87Tt -27i/3)cm. Thoi gian vat di
dugc quang duong S = 2 + 2V2 cm ke tu
liic
bat dau dao dgng la:
A.
1/12
B.5/66
C. 1/45 D, 5/96
^hdn
tich
vd
hit&ng
dan gidi
Ta
CO

HQC
dat diem toi da Vat It, t4p 1-Le V&n
Vinh
Vi
du 9:
(Trich.
de thi thu truang chuyen Nguyen
Trai
Hdi Duong Idn 2
nam 2013):
Vat
dao dong dieu hoa theo phuong
trinh
x = 5cos(107rt -
^)(cm).
Thoi
gian
vat di dugc quang duong 7,5cm, ke tu
liic
t =0 la:
A.
—s
15
15
C.
30
D.
— s
12
<Phdn

dupe
quang duong 5 cm.
De vat di
dupe
7,5 cm ke tu t = 0 thi vat ^
phai
di them 2,5 cm nua.
Tu
hinh ve ta thay x = 2,5cm = — .
Vay
thoi
gian can tim la:
t
MN
=
t
-1
+
1 ^
=
J-S
(0->A
>
Chpn
dap an D
A,=W)+t^^
4^ ^2 12
vi du
10:
(Trich

=^
tj
-1,
= 2,5T +-
^
T 2 ^ ^ 4
Cty
TNHU
Ml\-nWHKhau-^
-20
-IOV2
o
\OsI2
20
»
* r
1;
r
• f •
1
1
1
J
r"
1
J
1
1
1
1

-
2072(cm)
Vay
tong quang duong vat di
dupe
la:
S = S, + S2 = 200 + 40 - 20y/2 =
21
l,7(cm)
Chpn
dap an A
m
BAI TAP VAN DUNG:
Cau
1.
(Trich
de thi dai hpc nam 2013): Mot vat nho dao dong dieu hoa voi
bien
dp 4cm va chu ki 2s. Quang duong vat di
dupe
trong 4s la:
A.
8 cm B. 16 cm
C.
64 cm D.32 cm
'Phdn
tich
ra huang dan gidi
At
4

C.
50
+
5V2
(cm)
B.
40 + 5N/3 (cm)
D.
6O-5V3
(cm)
45
Bf
quyei
on
luyfit
thi dai UQC dat
diem
toi da Vat It, tap 1-U Van VmR
i'hdn
tick
vd
hudng
dan
gidi
Cach
1: Giai
theo
phuong phap dai so
Chu ky dao dpng: T = — = — =2(s)
CO

chieu
duang.
- So chu ki dao
dpng:
=
5V3cm
>0
tl3-ti,5
13
-1,5
N
= —=
T
At
J _ 3 17 17
6.2 12 12 12
- Vay thoi gian vat dao dong la T va At' =
5T
12
- Quang duang tong cong vat di dugc la: S^t = ^nT + S^,' = + S5J
12
Voi:
ST = 4A = 4.10 =
40cm.
fVi5Vi3
> 0
Vi
At<I
2
^13 - Xl,5

Vay: SAI = Snx + SAI' = 40 + 573 +10 = 50 + 573 (cm)
Chpn dap an A
Nh^n
xet: Cdc ban cd the su
dung
3
each
neu
trong
bai VI DU MAU van
gidi
ra
nhanh
chong.
0 day bai
todn
duoc
gidi
theo
edch
true
quan,
dua vao
hinh
ve.
^gu 3: (Trich de thi thu chuyen Nguyen Hu? - Ha Dong Ian 2 nam 2013)
MQt
vat dao dpng dieu hoa voi bien dp A, chu ki T. Ti
sogiiJa
quang duong

6 T 6 3
Quang duong Ion nhat ma vat di dugc trong — la:
6
Simax
=2Asin^ = 2Asm- = A
\^
1-cos —
Slmin =2A
_S^3, 2A + S,
= 2A
2A + A
1 ^
1-cos —
6
=
A(2-73)
3
2A +
A(2-73)
4-73
Chpn dap an D
Cau 4: (Trich de thi thu THPT Phiic Trach - Ha Tinh Ian 2 nam 2013)
Mgt
vat dao dgng vdi phuong
trinh
x =
472cos
cm. Quang duong
v^t
di tu thoi diem t, = —s den tj = 6s la