I 8,8cm / s.
(Di thi tuyin sinh dqi hoc mon VQt ti ndtn,20l4)
Hming ddn gidi: Bi0n d0 A:6cm, tdn s6
g6c o: nradl s.
-1a^A)ft
Tins6: " /=_ =- 2rc 2n =0,5Hz.EdpdnAsat.chu ki: r :4 -2n -2s. D6p 6n B sai. chu ki: r :4 -2n -2s. D6p 6n B sai.
ofii d2x i d2x
Gia tdc: a: : -6r2cosnt.
dt2
DO tcrn cgc tlai cua gia tlic:
a^u* = 6112 = 59,l6cmls2. E5p 6n C sai.
vdn t6c: 'dt ,:4: -6xsinnt. T6c d6 cuc dai:
v-u : 6n = 6.3,14 = 18,8m I s. Ddp dn D dilng.
IIANG 2. Edi t$p srt' dyng phuttng phdp
ndng ltqng
Ifti giAi c6c bdi tfp dpng niy cdn:
- Vfln dr,rng c6c c6ng thirc tinh dQng ning, th6
n[ng, co n[ng vd dinh 1u0t bAo toin co n[ngcho vflt dao dQng tli6u hda. cho vflt dao dQng tli6u hda.
- Ap firng c6c c6ng thuc tinh nlng lugng cua tp di6n, cuQn cim vd tlinh luQt b6o todn ndng
lugng cho mpch dao <lQng diQn tu di6u hda(dao rtQng diQn tu tU do). (dao rtQng diQn tu tU do).
*fni dV 4" Mat mach dao ddng I-C tl twimg dang c:o dao dpng tiiiu hr)u cli1n dr tqr do t,oi rli€n tlch ctrc dqi la Qs va ddng didru cryc dai
trong ntqch ld {r,. Dao ddng cliAn fii' ttr dotrong ruach cd chu ki ld trong ruach cd chu ki ld
A. T =3nQo . B. T:3nQo .Io Io Io Io 2nQ, C,T= . L). I 4nQo --. Io Io
(Di thi tuyin sinh dqi hec nt6n l/dt ti ndm 2{)14)
Ilwlmg ddn gidi: Ning lugng lon nhAt cua tq
diQn: Wg**uu :9. N[ng lugng 16n nh6t cua
2C
r12
cuQn ddy: W-@u*) : ":o . Theo dinh ludt bio2 2
tolrn n[ng lugnB iliQn tu: Wc@*):Wr(^u*y Dod6: Q& -Lr& suvra rC=%
2C2r&
Chu ki: T = 2nJ LC = 2nQo
Io
NhQn xit: Ta c6 thti giai bdi ndy ng6n gon
hon nhu sau:
( ;-
l_ z1L
ra c6 ] ! =, =2:Q . Dap an c dilng.
I o,:!!- Io
la
*fni dU 5. MOt vqt nho khdi lurmg 1009-.; -.;
clao dong di)u hoa yo'i chu ki 0,2s vd co ndng
td 0,18J fu6c th€ ndng tqi tti trf cdn bing);
lriy, x2 =1t). Tqi ti dp 3J1cm, ti sd dong,1 ,1
nang va tne nang la
A. 1. 8.4. C. 3. D.2.
(Di thi nyAn sinh tlqi hpc mdn VQt li ndm 2013't
TO6N HQC &o..&rr*roa*66a*s*reoa$cree.e!
* cfrr,iug '*'oa*66a*s*'*""'*'*u"*"'@'Gao'!oeoe'**+"0*{!60!Gss '-@dcl'silr|'
Hudng ddn gidi: Thi5 ndng cira vQt tai li tlQ x .r I . I (Zr\' OAng: W, =-mo'x' - -ml - | xL 2 2 \r)
Khi thay n2 :I0, m =1009: 0,1kg vd
x = 3'l-2cm : gJi.to-' m. ta dugc:
t (1-\2
w, ' 2 =!.s,1.1{l \0,2., .(rJr.10.) = o,oer
Co nlng cira vflt tai li d0 x ld:
W :W, +W, =9,191
DQng nlng ctra vflt tai li d0 x bing:
Wa =W -W = 0,18-0,09:0,09J
wd 0,09
=-=I.
w, 0.09
Ddp dn A &ing.
*ffri dal 6. Mot t'dt crs khdi lrong 50g, dao
-.;
dong dieu ltds vcri bi)n dp 4cm vd tdn ,so gdc 3rad/s. ilAng ndng ap clai cila vat lit
1\. 7,2.104J. B. 3,6J. C. 3,6.10-4J. D. 7,2J.
Ilrbng ddn gidi: DQng ndng cpc d4i bing co
n[ng ctra vQt dao tlQng di6u hda. Ta c6:
rrr _ mal2 Az rl almu\ - ^ Z Thay s6 m=5Og =5.10-2kg, at:3rad I s, A = 4cm= 4.10-zm, ta dugc: 5 .lO-2.32 .( 4. I 0-2 )2 trl \ / :3.6.10-4J. n/d1mu1 - - Z Ddp dn C dung.
DANG 3. Bdi t$p $An qaan ttin luc keo vi
Khi gini c6c bdi tpp dpng ndy cdn phdn biQt
luc k6o v6 v6i lgc din h6i cta ld xo:
- Lgc k6o v6 c6 cllc di6m ld 1u6n lu6n hu6ng
:. , ^ ,J.
vC vi tri cdn b[ng, lim cho v{t dao dQng
quqnh vi tri can.bing (c6 th6 S6rg di6u hoa).
Ching hpn, d6i v6i con l1c dcrn thi lqc
P, =-mgsina ld llrc k6o vC atr goc a lon.
N6u vflt dao clQng ctiOu hoa thi lUc k6o v6 ti 19
v6i li <lQ vd trSi ddu, -F - -lu.
- Luc k6o vC ta hqp lgc cira c5c lgc t6c dung vdo vft dao dQng di€u hda. Trong sti c5c lgc
tl6 c6 lgc cldn h6i ctra ld xo hoflc kh6ng. Vi
th6 md c6 s1r kh6c nhau gifia lgc k6o vA vd
lgc ddn h6l cira ld xo.
- Lai c6 nhirng h0 dao dQng di6u hda, trong
tl6 kh6ng c6 phdn tu cdq tr(rc ndo cira hQ loxo. Con 16c don, khuc 96 n6i bpp b6nh tr6n xo. Con 16c don, khuc 96 n6i bpp b6nh tr6n
m[t nu6c,... li nhirng hQ nhu vfy. D6i voi
c6c h0 ndy, khi dao dQng nh6 luc k6o v6 vdn
c6 dpng F = -lu, nhrmg khdng c6 bin ch6t
cria lgc ddn h6i.
*fU d{r 7: M6t vdt vrhd khrii tuqrng 5009
dao d$ng didu hda Cao'i titc dlrng c*a lrc keo
,A co biir.t thu'c 17 = -0,8cosar(N). Dao
d$ng cua vrjt t'i hiin d6
A.8cm. B.6cm. C. 12cm. D. 10cm.
(Di thi tryt€n sinl't dqi hoc ru6n Vat ti nrtm 2$12)
Ilmimg ddn gi,fii: Phucrng trinh cira vft dao )2-
dQng <Ii6u ha" *",! = F, trong d6 x ld li tIO
dtz
cira vft, F 1d lgc k6o vA. Ta c6: d2x m _ : -0.8cos4l suy ra dt2 d2x 0.8 0-8 -=- cos4l-- cos4t dtz m 0,5 huu d'* = -l-6cos4r . " dtz
Phuong trinh trCn cho nghiQm:
x : 0,lcos(+t + 9) (m). Bi6n d0 dao clQng
cira vft bing 0,1 m hay 10cm. Ddp dn D dung.
*fU dg 8. Mgt con ldc don dang clao clgngdiiu hda t,oi biOn et7 gdc da tqi nrti co gia toc diiu hda t,oi biOn et7 gdc da tqi nrti co gia toc tt'ong trudng ld g. Bi1t lqrc cdng ddy,tm nhtit
bdng 1,02 ldn luc cdng dfr , nko nhdt. Gia tri
cila as ld
A. 3,30. B. 6,60. C. 5,60. D. 9,60.
\De, thi tuyin sirth dqti hac mdn VQt ti ndm 20t t) Hming ddn gi,fii: Ta ph6n tich trgng lgc F
thAnh hai thdnh phin: Thdnh phAn { theo phucrng vu6ng g6c qu! d4o, thdnh phan E
.;, A
ti6p tuydn v6i qu! dao (hinh vE). Thdnh phdn
E @o do lon P, = mgsina ) chinh ld lyc k6o
vC vd ldm cho con 16c dao dQng di6u hda khi
g6c lQch a nh6.
fffi ffi( .""**u.oo'sdo'.ss6! &o{6.-"-.-" "@.o r...' s o +.qs&}!..*..or*.&
Hqp lgc cria llrc cdng i vd lgc thdnh phAn
H aOne vai trd lpc hu6ng tdm gifi cho vft
chuyi5n dQng tr6n cung trdn. Ta c6:
T-P:*" har, - mv2
,. I ,,T-mgcosa: , (l)
Theo dinh luflt bio todn co n[ng thi: mv2
+ * ngl (l- cosa) : mgl (l- cosao ) 12;
).
Trong do as ld bi6n tlQ cria con l6c clcrn.
Tri (1) vd (2) rft ra:
T : mg(3cosa -2cosas) (3)
Tt (3) suy ra:
Khi a=0 thi T:T^u*:mg(3-2cosag);
Khi a: ao thi T :T^n: mgcosdo.
Theo it6 611. 3= - Tr^, mg(z -zcosao) :t,02
mgcosd,s
Giai ta ta tlugc cosds =0,9934 , vay
do = 6,60. Ddp an B ilting.
*Thi dg 9. Cho hai dao dgng cimg phuang,
vni cdc phuong trinh ldn tu'qt ld
x, = Arcos(att + 0, 35)(cm)
vd x2 = ,42cos(at -1,5'7)(cm). Dao d1ng
tiing hqp cila hai dao dQng ndy cd phuctng
trinh x=Zlcos(ai +e)(cm). Gid tri cqrc dqi
cfia (A1+ A2) gdn gia n'! ndo nhdt sau ddy?
A.35cm. B.40cm. C.20cm. D.25cm.(Di thi tuyin sinh dsi hoc: mr)n Vdt li ndm 2014) (Di thi tuyin sinh dsi hoc: mr)n Vdt li ndm 2014)
Hwlng ddn gidi: Ta c6:
2o:@(cm).(1)
Ap durrg b6t ding thric Cauchy:
/r/
"*r-JAa, , (JA"A,)^,* hi Ar=Az.
Thay 1= A, vito (1), ta dugc:
4 : h x 17,5cm. YAy (4 + Ar)^*= 35cm.
Ddp dn A dilng.
*Thi du 10. Hai daa dQng cilng phuong cophuong trinh xr = lrcosl n *! l(.-) vd phuong trinh xr = lrcosl n *! l(.-) vd
\ 6/'- ( n\. - ( n\.
.rz - =6cosl Ll\til-: l(cm). Dao dQng tu|ng hqp
\ L,/
c*a hai dao dAng nay co phmmg
trinhx: Acos(xt+p)(cm). Tha1, d6i A1 cho
ddn khi hi1n tI6 A dqt gid tr! cqc ti6u thi
A. rp:xrad. B. e:-lrad.J