Solutions_to_Assignment__1

# Solutions_to_Assignment__1 - ﬂed,4/25 93/” ﬂsrxynmf...

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Unformatted text preview: ﬂed-,4; /25' 93/” ﬂsrxynmf #/ Jae Mangy I7’ym 20/1. @ 21/31)92, 59/5'6 ﬂax The function x = (0.6 m)cos [(3n rad/s)t + n/3 rad] gives simple harmonic motion. At t = 2.0 5, what are 1:; (a) displacement, (b) velocity (c) acceleration and (d) phase of the motion? Also, what are the (e) frequency and (f) period of motion? An oscillator consists of a block attached to'a spring (k=400 N/m). At some time t, the pOSition (measured from the system’s equilibrium :1 a: location), velocity, and acceleration of the blpck are x = 0.100m, v = ~13.6 m/s, and a = —123 m/s. Calculate (a) the frequency of oscillation, (b) . the mass of the block, and (c) the amplitude of motion. 'l- l- l" I -| I ‘1 v : .x -.., A simple harmonic oscillator consists of a block a of mass 2.00 kg attached to a spring of spring :4 constant 100 N/m. When t = 1.005, the position and " velocity of the block are x = 0.129 m and v = 3.415 ‘ ‘ 1 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? -i. .1 .4} i. 2: iii? A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has a period 1.0 s, at what amplitude of motion will the *2 block and piston separate? (b) If the piston has an ” amplitude of 5.0 cm, what is the maximum frequency for which the block and piston will be in contact continuously? Erér Two particles oscillate in simpleﬂbggmggggumgﬁign.ilgﬂ9 a common straight line segment of length A. Each particle has a period of 1.5 s, but they differ in phase by n/6 rad. (a) How far apart are they (in terms of A) 0.50 s after the lagging particle leaves one end of the path? (b) Are they then moving in the same direction, toward each other, or away from each other? A 4.00 kg block is suspended from a spring with k = 500 N/m. A 50.0 g bullet is fired into the block from directly below with a speed of 150 m/s and becomes embedded in the block. (a) Find the amplitude of the resulting simple harmonic motion. (b) What percentage of the original kinetic energy of the bullet is transferred to mechanical energy of the oscillator? An oscillator consists of a block attached to a the position and a = ~123 m/s? and acceleration of the block the frequency of oscillation, m u i r /b t.1 l e.i mu .101 I te S e w s m/ 0m 6 SE . t 3 CS 1 A Y _ Sr . Y: \let mhiv /tC N O, mlm Oon OrVO 4f 1 __ r. kd)O (en r0: gui nstx iaa IBCE Pmor Slxla (b) the amplitude of motion. (c) and (a) the mass of the block, Calculate 3.415 the position and 0.129 m and V 1.00s, (a) What is the amplitude of the oscillations? A simple harmonic oscillator consists of a block of mass 2 00 kg attached to a spring of spring velocity of the block are x constant 100 N/m. when t m/s. 35 (a) (b) position and (C) velocity of the O s? What were the block at t a7? Z A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has a W period 1.0 s, at what amplitude of motion will the block and piston separate? (b) If the piston has an Z%’S: amplitude of 5.0 cm, what is the maximum frequency for which the block and piston will be in contact continuously? r Cc'amrwéelf,’ V. . , L. A.9 a common straight line segment of length A. Each particle has a period of 1.5 s, but they differ in phase by n/6 Two particles oscillate in simplgﬂh 0.50 s (in terms of A) after the lagging particle leaves one end of the path? How far apart are they (a) rad. toward (b) Are they then moving in the same direction, or away from each other? each other, '55 \ l I I l 0 [i . X L), i . 5 , | LC ; . § i . 1 3/1; _--_._‘ .-. q: W l x ‘2 1 l | WM ,[ H What percentage ) b ( (a) Find the amplitude of the k = 500 N/m. A 50.0 g bullet is fired into the block from directly below with a speed of 150 m/s and becomes A 4.00 kg block is suspended from a spring with of the original‘kinetic energy of the bullet lS transferred to mechanical energy of the oscillator? resulting simple harmonic motion. embedded in the block. m 6 S’Q'é‘ogwf .43 mfnmf #1 #2/ 2|. A lUO—g mzm ix attached to u spring of constant k = 5.6 N/m and set into osciIlulmn with .nnplitude A = 25 cm. Dclcrmine (u) the frequency in hertz. lb) the period. (c) the maximum velocity. and (d lhennxin nhr‘ ’ lh‘. ' . /é : N/M ) 1 ll” «Lem cxpnng 9‘ 6 26 A particle undergoes simple harmonic motion with amplitude 25 I # cm and maximum speed 4.8 m/S. Find (a) the angular frequency, 1 (b) the period. and (c) the maximum acceleration. /\ 3 8 u ‘L‘ N n V 00 l \ jo p E 1% 9 CAL/5 goo 7/42 :) £14599) 2 62-3 746%» 60 32‘ A wheel mtates at the rate ul~ (100 rpm. Vicwcd from [he cdge. a V paint on the wheel appears to undergo simple harmnnic mutimr ' C4.) : L : ‘ l’rm ucncy in HI. and (b) the angular t'rcqucncy ; _. _ Wh u \re ( 1) [ha 1 .f / ' for [his SHM‘.’ 42. A muss m slides ulnng a frictionch hnrimnml surface at speed 1",. H slrikw uspring nt'consmm k amuchcd m u rigid wall. a». >hmm m - Hg. I127. Al‘lcr :1 completely elastic cncuumcr with the .xpring. #' é/ [he mzm heads back in the dircclinu it came l'rum. In (cum (WA-.1”. nml \'.,. dc‘crminc (u) how long the mass is in contact with the Q We 5’ I»? spring and (h) lhc maximum cumprcssinn 01‘th xpring, ~ 22 I a a /' % A) 17/ ‘ f r0 em4 Car/77 V9,? avid Mia € ncunns.27 P b! 2 0(1),. Mm‘ﬂfv (cf/Qt Q, S.H 051/41 q ch%4d% U; 'ﬁ6037/ mozwzt/Iey' 0 :‘ V0 : ﬂ :3 R 54. H' J4me and Tarzan urc initially 8.0 m apart in Fig. 13.12. and June's mass is 60 kg. what is the muxinmm tension in the vine, and u! what point dues it occur? (:-€=25‘m- r“ 1 gm“: my % mum“ @(L /o;,‘/a1. 6 W GMWdM/w 7 WW p794 : é M02 m :- ymyﬁfq; : 2Mj4:XMj(Z-lf(€L—/cﬂj Am” 2 50 (9-?) 7‘ (K0) (9-9)2 (25‘ ~ 1/253/5) :25 :2 503M c. 56. A mass m is mounted between two springs nfmmlums k] and k, as \hown in Fig. [3.31. Shqg/‘Ihut the angular frequency of mcillulion is given by w : V(/\'| 7f- k3)/m. FIGURE 13.3] Problem 56 M 0/64 7V! ’2’?- _. . ﬂax *Z’Lx) Q”— M “yr/'4! @ 0"”? y’r/‘dﬂ @ WW ‘ u "7 A‘ I ' iF : mq/‘4J‘f‘ #9 «ﬁg, fie—)1 = m 253.22 54-1 4:2: 2 «- M2 ,. A” (7%] Y e C 1rdn dane a an rt q ane 3hor /W.lf H t Ia) +Sre e/\ tOl \J.ee SZCh / Ct d=a a e rt)r ca Htl\ 3A t rL .th niw SOC 0.10 I Cth? mmmmm Ai 6C) .2 L .ib?O n w (0 O I mlif., =rttO, ano , thmd neee Olch ipat t m l Cin nSSO u i fsde e s eV)a hiah T9(P (d) and (f) periO -~ 'mquerr" ...
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## This note was uploaded on 04/01/2012 for the course PHYS 125 taught by Professor Mohamed during the Spring '08 term at Waterloo.

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Solutions_to_Assignment__1 - ﬂed,4/25 93/” ﬂsrxynmf...

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