M = 20A (fl.Tr€n M dQr th€m vdt c6 khdi luong
m = 600 (d Dqr h€ thdhg tr€n mdt phdng nam
ngang nhd.n (hinh vd). Ban đu giii vdr M sao cho ld xo cd cJd đi l1 = 2lcm r6i thci nhe nhdng
thi h€ dact d\ng didu hdạ
l;
/ *LQ!-aa!oa!j M I
I ) Hdy vi€lt phaong trinh dao đng cia h€. 2) SaLt khi dao đng duoc 1,5 chu ki thi ngudi
ta cdlt di vdt m. Hdy vi€1 phaong trinh dao đng cr)ávdt cdn laị Móc thdi gian nhrt cit.
Ldi giiị 1) Tdn s6 g5c cfia h0 (M + m) dao dong di6u hda :
I 80-
ar- .t : l- = I0(rad/s).\ n+tt ! o,g \ n+tt ! o,g
Chu ki dao dong: r = 4=?=:=0,628(s)rol05 rol05
Phuong trinh dao d6ng: .r = Ạsin(10.r+q) (cm), vQn tdc v = 10.A cos(lOr+q). Tga dQ ban đu
cta hO : xo = 11 - lo = 1 (cm), cbn v6n t6c ban đu u, = g.
fasmq = I (cm) Itr0.Acosg = 6 ) A - l(cm) vh g:;
VAy phuong trinh dao dQng li : _r = sin(10/ + nl2) {clg:.)
2) Sau khi dao d6.ng duọc 1,5 chu kitt = t,-5.! = 0,3x(s)), vat 0 vi trf xr = -l(cm) tt = t,-5.! = 0,3x(s)), vat 0 vi trf xr = -l(cm) vd vAn tdc bang 0. Kd tt hic nhy tr& di chi cbn
minh M dao d6ng didu hba, vfi tdn sd g5c :
*= ^E:,tr =20(rad/s).
\rw !0,2
Phuong trinh dao dong : x = Asin(20r+g) (cm), vAn tdc : v =20Acos{201+<p) (cm/s)
-1-., . o
3'
Vi P'(y) < 0 v6i moi y e n6n P(y)
nghich bi6n trong nira khoAng
ra : P l6n nhat khi y = -], t,i"
vd do d5 rir (3) suy ra khi coscr = I rruu cr= 6oo-
2'
yQy gil,tr! l6n nhst cria p h p=
"r-1) [3/ = le1.27
Chrt ị Lric niy đ y them d6n h0 thfc_ (1) thidt lip 6 trOn, ta thdy rang khi cr = 600 thi
ffiD:lB = x = 90o vd do d6, hinh ch6p trtr
gi6c đu SABCD n6i tidp m6t cdu nm FI bdn
kinh R - Slr = +:*. Ngoii ra, hinh ch6p
22
tri gi6c .iet sABCD hic niy li mor nta khdi b6r
diOn tI€r: K = S.ABCD.S'trong d6 dinh rhrl sr{u S'
đi xircg vdi S qua mp(ABCD).
Nhin x6t 1) Bii to6n nly thuoc loai d6, tim cuc tri
mft hem sd luong gi6c, rrong d6 d6i sd 9 li sd do g6c nhi di6n cta hai mat b6n cira m6r hinh ch6p ni gir{c d?ụ
Tuy nhi€n, hdu hdt ldi giei chi chd f den vigc tinfr A9 tOn
cria g theo goc phing a & dinh mi kh6ng giii thich cdch xdc dinh goc phing nlU dign.
2)4"ef,L€r c6 2O ldi giai cho d6p sd sai vd gi6 rri l6n nhat c&a bidu thfc 1,. C6 ban rhi dih toiin saildac'bict
kdt lưn sai ldm h hnm P(tp) kh6ng c<i cgc dai v6i 0 < cr
< 600.
.3) Cnc ban sau day c5 ldi giei diing, vi nrong đi gon
gang.
Hn NOj t Nguyin Trudng Giang, lOAl, Torin, DHKHfN - DHQG Ha N6.i, Nguy€n ltnh Qwdn, LtA1. ITICTT-DHSP Ha Nọi ; Hi Tay : Le Ddc Hdi, ttl2,
TFIPT chuyOn Nguy6n HuQ, Tx. Hi DOng ; Irmh Phrtu :
NguydnTho Khi€m,11410, THPT ctuy€n V-rnh Phdc ;
Phri Tho : I* Bd Ltng, lOTotu1Triiu Anh Kh6i, Dinh
Dtlc Tlzdnh,1lA1, TI{PT chuy€n Hing Vuong, Tp, Vier Tri ; Hii PhDng : Itru Ngin Hd, li Trung Son, lA\
TIIPT NK Trdn Phri, Tp. Hii Ptrdng ; Thanh H6a: Ltru D*y\illr,11K2, THPT Lam son, Ddo Viat dfrng, ltA1,
THPT HAU I-6c I , Nguydn Vdn Inng, 12A4I, TIIPT
Luong D6c Bang, Hoang H6a ; Ngh6 An z Nguydn Ngoc Cudng,l2Al, THPT Phan B6.i Ch[u, Tp. Vinh ; Quing
Tri : Ngutin Trdc ViAt, Truong Song Hio, l2Al, U Tiin Tridn,llT, THPT chuyen Ir Qui DOn, Dd Qudc
Khdnh, lLAl" PltanTudn Anh,12A1, TI{PT chuy€n lr
Quf Don, Tp. Dn Nfog ; Lim Ddng : Nguydn Ngoc
Duy, L2 Toi{n, TIIFT thang I-ong, Tp. Dn lat ; Ddng IYai : Ngaydn Thd Nam, il Todn, TFIFT chuyen Luong
[-í,)
[-+', ra suv
.. I
la cosq = - 3,
{ --.