The time for one cycle of a periodic proc ybhl(/o4tnr 52sivq lyg b:.-4 o+xqness is called the

  For a periodic process, the number of cycles per unit time is callekzcqrq ,/yty 0d:/fm4d the

  For vibrational motion, theg 8 :d,+)dwhkqcnh;gyv5n1mu dp3;gu maximum displacement from the equilibrium point is caldhgu; 1y38knq)u5,mw :h vdn d +gpgc;led the

  A mass on a spring undergoes SHM. When the mass is at its maximum disp :oh(4e mxsx,rlacement fr xx,(mse: 4ohrom equilibrium, its instantaneous velocity

  A mass on a spring undergoes SHM. Whvsenbna 9i))s0 jws:b3 2+ xomen the mass passes through the equilibrium position, its instantaneous vevj ban 20b9sx:)s)nm s3i +ewolocity

  A mass on a spring undergoes SHM. When 0/e9ezynihrh)w 7q1x4 j( sir the mass is at maximum displacement from equilibrium hr/wq4hxsz9j1n7ei y)0ri (e, its instantaneous acceleration

  A mass is attached to a vertical spring and bobs up and down bp: i e:ht uu b7/qovxf;h2.rr2etween points A and B. Where is the mass located when if xorue:.:2qrv/27;u pbi hthts kinetic energy is a minimum?

  A mass is attached to a vertical spring and bobsi0d( qadsq krq9k8f-- up and down between points A and B. Where is the mass located when its kinetic energy is a m q -rskqd9a(8idfqk0- aximum?

  A mass is attached to a vertical spring and bofw6 oaf9r (.;/-b zc1ct4rb chch; jjmbs up and down between points A and B. Where is the mass located when its potential energyf1wzhc 4ctac o6r9; mfcbhj b/;.(j-r is a minimum?

  A mass is attached to a vertical spr+z8b e ;e nc:vxbrtpvm 8:l 6/:mzia;ding and bobs up and down between points A and B. Where is the mass located when its potential energy is a maxi vz8eizel+nar m8:cpvb:/ td:mxb; 6;mum?

  Doubling only the amplitude of a vibrating masq, -weaobrk/ 2p. e,rd)u0hkds-and-spring system produces what effect on the system's me ,r/do. wkp)er2u e, 0dqkb-ahchanical energy?

  Doubling only the mass of a vibrating massln667l:qip h uc ez2d j(.cd4l-and-spring system produces what effect on the system's mechanical:l upn2lzhje.6(di d c7c4 6ql energy?

  Doubling only the spring constant of a vibrating mass-and-sprid1n7 y od53vvang system produces ovvy7 15d3 dnawhat effect on the system's mechanical energy?

  A mass oscillates on the end of a spring, both on Earth and on the0yc12mhwe47xuwf g+x,4q z h v Moon. Where is the period the greatest?40f4whh,ewu vxx g+c y71 mq2z

  Increasing the spring constant k of a mass-and-spring system causes what eaa:qy**b yhw(n* 1kq kind of change in the resonant frea(ey:1aq *hqy*k *wbnquency of the system? (Assume no change in the system's mass m.)

  Increasing the mass M of a mass-and-spring system causes what kind of change iqp+ ne7mh1jk:n the resonant frequency of the system? (Assuph 1n7:jqm+k eme no change in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spring system causes what kinn2xfz epfbu32 4qm36 dd of change in the resonant frequency of the system? (Assume no other changes in the sys ef2f bm2d3qz36 pnxu4tem.)

  A mass $m$ hanging on a spring has a natural frequency f. If the mass is increased to $4m$, what is the new natural frequency?

  A simple pendulum consists of a masv(u un(lj*fu*om3bc)6a nime) ds5 /qs M attached to a weightless string of length L. For this system, when underg*j 3i*6/avqd n (cmb(u )nu msolufe)5oing small oscillations

  When the mass of a simple pendulum is tripled, the t(e:cvqqzj,(v ime required for one complete vibr (cvqqjv ,e(:zation

  Both pendulum A and B are 3.0 m longp;;pe6slmb6o gs0tq *x2iu(j . The period of A is T. Pendulum A is twice as heavy as pendulum B. What is the period ob6qo;(l2s es;giuxm*0 pt p j6f B?

  When the length of a simple pendulum is tripled, the time fxx-g jhu(m-g:a- xwy*m v)3eh or one complete vibrat-gmvygh)xjw -ea(xu* xm 3h: -ion increases by a factor of

  What happens to a simple penduluz; w-m7njd,l um's frequency if both its length and mass are increasn-uz;jm 7dl,wed?

  Simple pendulum A swings back and forth at twice the frequency xk3e4f( 63lcjecj xokz//r n .of simple pendulum B. Which statement is cokzfn6r3l4 j.ceex3x( //kj correct?

  If you take a given pendulum to ta 9igr+y e5o*x 4)nubvhe Moon, where the acceleration of gravity is less than on Earth, the resonant frequency of the pendulum w )bogu+9 *xirea 5y4vnill

  Curve A in Fig. 11-1 repres-wg.vfpc yd.8cs j6*fents

  Curve B in Fig. 11-1 6c2md, ,v)k35 r2ms gnxnltpwkv,s(qrepresents

  Curve C in Fig. 11-1 reprelt8 bmu5-;cwn sents

  For a forced vibration, the amplitude of vibratiowj*ae 6;fu r eylk9((, lkeg5zn is found to depend on the

  In a wave, the maximum disp,ca i(c04 nndh5ucc :llacement of points of the wave from equilibrium is called the wave'sacn:cld cu 45in,c 0h(

  The distance between successive crests on a wave is called the wax +bmo6q3r,)o n3hkjgw; mb3lve's

  The number of crests of a wave passing a point per unit time is called 0z5bxmvp6* hllf v0l+ the wave'svzvf6l h5lm0bl* +x 0p

  For a wave, the frequency times the /jt2sw qt)xuwpt+ x09wavelength is the wave's

  The frequency of a wave i m07/hz/hkg,mpyrv: bncreases. What happens to the distance between successive crests if the speed mhvgbz :pm / rh,0yk7/remains constant?

  A wave moves on a string with wavelength l and frequency f. A second wave oeykt;(;wm f3gg 4vrmol5v 6w5 n the same string has wavelength 2l and travels with the same velocity. What i35ym(w;g o5ftkmeg lvv; w46r s the frequency of the second wave?

  Consider a traveling wave on a shwpejwm+b 03qhn-)t84 *ocnbtring of length L, mass M, and tension T. A standing wave is set up.*8w h m3p)4t+h0n-eoqc nbj wb Which of the following is true?

  A string of mass m andi/4mgw; )y( 2xbeupwyf;ai y6 length L is under tension T. The speed of a wave in the string is v. What will be the speed of a wave in the striw ;bgum) 46 wy/if;yp y2aei(xng if the mass of the string is increased to 2m, with no change in length?

  A string of mass m and length L is under tension T. The spe nw62 5x7;um xrg6ny, xzqtld. wxlx6:ed of a wave in the string is v. What will be the speed of a wave in the string if the leng gnxxwq6x 7z u 5r:2l6xw;tlxnm.y,6 dth is increased to 2L, with no change in mass?

  A string of mass m and length L7-dbp *ccg3p82mzgpm is under tension T. The speed of a wave in the string is v. What will be the speed of a wavem7b2dp8c zgm3-gppc* in the string if the tension is increased to 2T?

  In seismology, the S wave is a transverse wave.knyudur z60 3ox/h9j ) As an S wave travels through the 0oh93 / rx)uynkd6zjuEarth, the relative motion between the S wave and the particles is

  In seismology, the P wave is a longitudinal wave. As a 8c 90n ledg+p+zp7jj xP wave travels through the Earth, the relative mo+z lj7jxgp 8nc9e +0pdtion between the P wave and the particles is

  The intensity of a wave isys +p.5bfqz (:terya +

  A wave pulse traveling to the right along a thin cordzdkh4 tq0 sr5z*eiwk.g7 0h:k reaches a discontinuity where the rope becomes thicker and heavier. What is th.h7kzdk0qzg5 st:kre i4hw0 *e orientation of the reflected and transmitted pulses?

  Two wave pulses with equal positive amplitudes pass each other on a strin*p*1/t k fdpmpl- zad3g, one is traveling toward the right and the other toward the left. At the point that they occupy the same region of space at td*da1 -mpf*t/3lp z pkhe same time

  Two wave pulses pass each other on a string. gs*c hzjj ls(;jli 4 +uixf (a)vn40f5The one traveling toward the right has a positive amplitude, while the one traveling toward the left has an equal amplitude in the negative direction. At the point that they occupy the same region of space at the0l j+suh jxg(s;j *c5nfzf)i4l4 v(ia same time

  Resonance in a system, such as a string fixed at both ends, occurs ( ix9tnegb isx1t4- g6odbi; 5when

  If one doubles the tension in a violin string, the fui*epy ,hy u79w5,eflmndamental frequency of that string will inceu,i5yw 9hfl7ym*e p,rease by a factor of

  What is the spring constant of a spring that stretches 2.00 cca24lft4tdqb3qm (b*fw48jwp j*( ry m when a mass of 0.600 kg is suspended 28rm(* lb (3jyabt qqtcw pjf4fdw*44 from it?

  A mass is attached to a spring of spring constant 60 N/m along a horizonxo85/qf 2gp p wki1,mktal, frictionless spom,gw5qk2 k /f xi81purface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is the amplitude?

  A mass is attached to a spring of spring constant 60 N/m alon v7ok5 *vi-gmzw:4qyg g a horizontal, frictionless surface. 4iv57z:kmvq yg*wg- o The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is the period of oscillation?

  A mass is attached to a spring of spring constant 60 N/m along a horizh o bi16fl6l( tl;fk6rontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is the fr(ikofllf 6rbt6 h6; 1lequency of oscillation?

  A mass on a spring undergoes SHM. It goes through 10 complete oscilla7lqjdy dm 1/,f- 5cidjtions in 5.0 s1-j,lddm 7/ cfyijdq 5. What is the period?

  A mass vibrates back and forspe3lcmat (kf 4* 1hl8th from the free end of an ideal spring of spring constant 20 N/m with an amplitude of 0.30 m. What is the kinetic energy of this vibrating mass when it is 4 pcktml8le13*(hs af0.30 m from its equilibrium position?

  A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a hori 0cb* 4xk6.la8 .m,rpwroiwllzontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the total energy of the sys pl8m 4w.w6k rrx,0b*.clail otem?

  A mass undergoes SHM with amplitude of 4 cm hbmo01*la nj lp9873hbbfh*yr9q ml*oq( ey*. The energy is 8.0 J at this time. The mass is cut in half, and the system is again set in motion wmyyqbl br* *ahm lh 99njb1*le oop03h78( *fqith amplitude 4.0 cm. What is the energy of the system now?

  A 0.50-kg mass is attached to a spring of spring constant 20kz(bs1280ptul*nqu i h0s ko wh9 tm91 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed ouqn9*i0 0ultk8zsho(p2k9hw 1s1bt mf 1.5 m/s at the equilibrium position. What is the amplitude of vibration?

  A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a.mxfnlf -wxmah.)- nu, a6d/r horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. At what location are the kinetic energyx f.w)/r,ua-h mfn6xlan .-md and the potential energy the same?

  A 2.0-kg mass is attached to the end of a horizo4 q554j+ck86s q9 a)si,mhwreqnd qxo(u(g dtntal spring of spring constant 50 N/m and set into simple harmonic motion with an amp4 8s6wd hoqqmctasge(9r i+dqx5j n,()4kq5ulitude of 0.10 m. What is the total mechanical energy of this system?

  A 2.0-kg mass is attached to the end of a horizontal spring of spring consta tuizf,upmt5 1+ yy s4dp/:kw;nt 50 N/m and set into simple harmonic motion with an amplitude of 0.10 m. What is the totwz k+dy i,;u1t 4/s tf:pu5mpyal mechanical energy of this system?

  A mass vibrates back and forth from the free end of an ideal spring of spring.(sts),)h ,zn urjvju constant 20.0 N/m with an amplitude of 0.250 m. What is the maximum kinetic energy of zvtj s )n(jrhuu).s ,,this vibrating mass?

  The mass of a mass-and-spring system is displaced 10 cm from its equil n.9xzjgm x7e7ibrium position and rel jx7gm 9xzne.7eased. A frequency of 4.0 Hz is observed. What frequency would be observed if the mass had been displaced only 5.0 cm and then released?

  A 4.0-kg object is attached to a spring of spring c4k(cukq r+go yl.a /z2onstant 10 N/m. The object is displacedrk/qoz.ku4 2l+ a(cyg by
5.1 cm from the equilibrium position and let go. What is the period of vibration?

  A 4.0-kg object is attached to a spring of sprih 82m6x7ai bfnng constant 10 N/m. The object is8a mfh6 bx72in displaced by
5.1 cm from the equilibrium position and let go. What is the frequency of vibration?

  A 2.0-kg mass is hung from a spring ofub./tl2 5-hyh-bt auh spring constant 18 N/m, displaced slightly from its equilibrium position, and released. bu-atu blhh25h -/yt.What is the frequency of its vibration?

  A mass is attached to a spring. It oscillates at a frequency of 1.2z)m3q js 2atho8nk -ltg2 .dc+fs-ve*7 Hz when displaced a distance of 2.0 cm from equilibrium and releasedhnev3tj l*za2+t- s2q.kd -mcg8 so)f. What is the maximum velocity attained by the mass?

  Two masses, A and B, are attached zlk:zfh,/ yoyoxf2x2ts 7g.n* yhr;: to different springs. Mass A vibrates with amplitude of 8.0 cm at a frequency of 10 Hz and mass B vibrates with amplitude of 5.0 cm at a frequency of 16 Hz. How does the maximum speed of A compare to th:hyf y*z7z:h,f x2s2rk xntoygl.o; /e maximum speed of B?

  A 0.30-kg mass is suspended on a spring. In equilibg:ylmv cdrbdn ;u.(5c:9 w, ocrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Calculate the pedgy ocw:l .dr,b u(v;:5mn9ccriod of oscillation.

  A 0.30-kg mass is suspended on a spso-+eqa7rf-/ 5 no y5zbrb+f cring. In equilibrium the mass stretches the sprin+ r /fqnzrb obys-oa 7cf5e-+5g 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Calculate the total energy of the system.

  A 0.30-kg mass is suspended on a spring. In equilibriutn:v 7 5ja+ctxm the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Write down its equationa t:x7 +t5jncv of motion.

  An object in simple harmonic motion obeys the folli ,z4hfhcg/ e(owing position versus time equat hzifc/h e,(g4ion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeyskr(lat6iy. 5(tf( i ai the following position versus time equatit( ikrilf( 6t aa.yi5(on:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following position versus time eqr+n3 vux) 6f0bdyr c/lu3 +)/dfb6 rnu rx0lyvcation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes simple har 8:nhdh9gc *0aqudwr /monic motion according th0q w rh/a:dgun*c 89do the equation $y = 0.50 \; \sin (18\pi \times t)$ where y is in meters and t is seconds. What is the period of vibration?

A 1.5-kg mass attached to sprin x:dv,kf4b,ziwug .)ug with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the mass is released from rest at x= 10.0 cm. (That is, the spring is stretched by 10.00 cm. xkv,d,z gb.u4wfu:i))
(a) Determine the frequency of the oscillations.
(b) Determine the maximum speed of the mass. Where does the maximum speed occur?
(c) Determine the maximum acceleration of the mass. Where does the maximum acceleration occur?
(d) Determine the total energy of the oscillating system.
(e) Express the displacement as a function of time.

  A pendulum makes 12 complete swings in 8.0 s. (a) What are its fxv-.p5hy s 2jnrequency and period on Eartn-.xhjy s5v2p h?

  A 3.00-kg pendulum is 28.84 m long. What is its period on Eartwya.* qrv;yfv( iaqn) ; ;0wzgh?

  A pendulum has a period of 2.0 s on Eart;sl1m:a)jdduks;+ er:(h/ cpp gkq ;k h. What is its length?

  The pendulum of a grandfather clock is 1.0 m long. av7w* aai7/6iirkwo2 What is its period on the Earth/k vaio2ir7i6awa w7* ?

  The pendulum of a grandfather clock isa) c2ss/i,( xcig ke:v 1.0 m long. What is its period on the Moon where , vcgi)exik sc(s:2/athe acceleration due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-kg spherical mass attached fwy 1z1o(s5bn*8balex*af8nto a massless string. When the mass is displaced slightoas 8z1y(f bnbwa51xn*8* lf ely from its equilibrium position and released, the pendulum swings back and forth with a frequency of 2.0 Hz. What frequency would have resulted if a 0.50-kg mass (same diameter sphere) had been attached to the string instead?

A simple pendulum consisting of a 20-g mass has initial anguf( y,,ybe+tf zlar displacement of 8.0e. It oscillates with a period of 3.0,eyyt+( ,bffz0 s.
(a) Determine the length of the pendulum.
(b) Does the period of the pendulum depend on the initial angular displacement?
(c) Does the period of the pendulum depend on the mass of the pendulum?
(d) Does the period of the pendulum depend on the length of the pendulum?
(e) Does the period of the pendulum depend on the acceleration due to gravity?

  Figure 11-2 is a "snapshot" of a wave at a given time. The freque vb0 .zn-9mf e;k,mfake c(c4dncy of the wave is 120 Hz. What is the amplitude? vke,d.amc ;9kefz(0bfc n-m 4

  Figure 11-2 is a "snapshot" of a wave at a given time. T l /r,7xas)a1ea9fticlu8kh l4i s42ahe frequency of the wave is 120 Hz. What is the wa4asll 7ea t/k u9f,hl 8i2ax)i1c ar4svelength?

  Figure 11-2 is a "snapshot" of a wave at a given time. The fw 8hzpwy mi9qnjf/: ;s9pse+,d y6. wbrequency of the wave is 120 Hz. What is the wave speed/s8 wqh6y+w9 nzi;spf 9:epwj,ym.db?

  What is the frequency of tskq7 k50f*op*s kxo4a wave which has a period of 6.00 ms?

  What is the period of a wave with a frequency of 1500 Hz++bp3xuq j2i w?

  What is the wave speed if a wave haxob3(kxx7*w+ w guqn9s a frequency of 12 Hz and a wavelength of 3.0 m 7q9 nx bxkgu*wx3+w(o?

  What is the velocity of a wave that has a q 7l:sxpmr b.ut58evz xcb 9*n0i-go8wavelength of 3.0 m and a frequency of 12 Hz?i8.xb:q 9*c7-xmu trz go5p08vnesl b

  What is the frequency of a 2.5 m wave traveling at 1400 3t b q//2 ph5uovbfdt,m/s?

  A piano string of linear mass density 0.0050 k2m-k* c+4v:r b zywsogs91quqg/m is under a tension of 1350 N. What is the wave s1qv4:yomurg*q ws 2k+-9bzc speed?

  A string of linear density 6.0 g//sdg rv(u+pws- 23ms ym is under a tension of 180 N. What is the velocity of propagation of transverse waves along v s dwsr-y/gu(sm+3p 2the string?

A wave whose wavelength is ko3nbml.uq-k :zq i 5(c4vmt+0.500 m is traveling down a 500 m long wire whose total ma:q mk t.moukvqz45i( l- bcn3+ss is
25.0 kg. The wire is under a tension of 2000 N.
(a) Determine the velocity of the wave on the wire.
(b) Determine the frequency of this wave.

  The velocity of propagation of a transverse wave on a 2.0-m long s0, 4cjjgkizh +tring fixed at both ends is 200 m/s. Which one of the fol4jk+hjz,c gi0lowing is not a resonant frequency of this string?

  If a guitar string has a fundamental frequency of 500 Hz, wh+*sy d7cl0 yp;k;ktguich one of the following frequencies can set the string into resonant vibr;l dkg0+ckpy7su* yt; ation?

  A stretched string is observed to have four equal segments in a bh-b6ouuzl9r)x -i- jstanding wave driven at a frequency of 480 Hz. What driving frequency will set up 9jx)6u- obhrb- zui l-a standing wave with five equal segments?

  A string, fixed at both ends, vibrates at a frequep*ik4dj x4 u n1ln5*rcncy of 12 Hz with a standing transverse wave pattern containing 3 loops. What freqxu i145*jcnr*4npk l duency is needed if the standing wave pattern is to contain 4 loops?

  A string of linear density 1.5 g/m is under a tension o:(m9f ic *hjegf 20 N. What should its length be if its fundamental resonance frequency is 220 H ei(gj c:fm*h9z?

  Find the first three harmonics of a string of linear mass density 2.00pr7pk;b3*. r-k(;txt kgc gu f g/m and length 0.600 m when it is subjected to tensio;rk bp;7gtfupkgc- kx( t.r3*n of 50.0 N.

A string of length 2.5 m is fixed at bothc:o,q l8a nl1q ends. When the string vibrates at a frequency of 85 Hz, a standing wave: q ,n1llqcoa8 with five loops is formed.
(a) Determine the distance between two adjacent nodes.
(b) Determine the wavelength of the waves that travel on the string.
(c) Determine the velocity of waves.
(d) Determine the fundamental frequency of this string.