The time for one cycle of a periodic process j +ydyze4 .,cya)x6vi is called the

  For a periodic process, the number of cycles per unit time is calledd19pakeu36 f *n(z emu0 c6uib the

  For vibrational motion, the maximum displaceyzsg(, d4zdsgn*j7 cn)(ym 3e ment from the equilibrium point is called then)ez*gmd7 z (3yysncjs, (g4d

  A mass on a spring undergoes 99f+gjgo mtq )zzdrnqq0.-b)f5k e)m SHM. When the mass is at its maximum displacement from equilibrimgfq fmjogtq9 )z. r)k q)+n e50d9bz-um, its instantaneous velocity

  A mass on a spring uc(q,/b s 3xjxendergoes SHM. When the mass passes through the equilibrium pos (bcx,s3jx/eqition, its instantaneous velocity

  A mass on a spring undergoes SHM. When the mass is at maximum dis9/d;5wijeic p placement from equildiic;w5p/ 9e jibrium, its instantaneous acceleration

  A mass is attached to a v7x:n;n5 xrwq*+h pvynamo9 k z31/ oexertical spring and bobs up and down between points A and B. Where is the mass locate 7 anxvy 9h: mon+1/k3*wnzqx5p;roe xd when its kinetic energy is a minimum?

  A mass is attached to a vertical springg d sz1ey.n3xscw; t+8 and bobs up and down between points A ane;sz x8y1ts .+dg3ncwd B. Where is the mass located when its kinetic energy is a maximum?

  A mass is attached to a vertical spring and bobs up and dott x e/c rd3v38hg1f2u+2egmiwn between points A and B. Where is the mass located when its potenti/ee3 t+t3 gxv1h8d2 im2crugfal energy is a minimum?

  A mass is attached to a vertical sprincjilw(y d08 u)czf:e4g and bobs up and down between points A and B. Where is the mass located when its potential ez fwdcce l8) ui4(:0yjnergy is a maximum?

  Doubling only the amplitude of a vibratinc,sx0/v+d 1xebpu9d tg mass-and-spring system produces what ecxb/pv t9u0, es ddx1+ffect on the system's mechanical energy?

  Doubling only the mass of a vibrating mass-and-spring system produces whatpfky/4pu-sqv2rw : 6u effect on the system's24v up-u/:pqkw ryfs6 mechanical energy?

  Doubling only the spring constant of a5h w6+qvddl4l vibrating mass-and-spring system produces what effect on the system's mech d6l45vw +lqdhanical energy?

  A mass oscillates on the end of a spring, both kv.vnmj3bo .4on Earth and on the Moon. Where is thbn4vk.jvo. 3m e period the greatest?

  Increasing the spring constant k of a mass-and-spring system causes wha f.mb fh)zmxma7/ r4d4t kind of change in the resonant frequency of the system? (Assume no change in the system's mm a4zfmd/bmr.74h) fx ass m.)

  Increasing the mass M of a 4hin ,g,)f k dtz08jxa *-dxlgmass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no cha 8k,x*d0 )lhant jgz4 x-df,ignge in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spring system c4szm :cb jpj);+clsn7 auses what kind of change in the resonant freque4 sjjc+nzp;7b) :c mlsncy of the system? (Assume no other changes in the system.)

  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 u* v3)td5jbxn z)eo o3mass M attached to a weightless string of length L. For this system, w)j5vo3b etn zx* 3d)ouhen undergoing small oscillations

  When the mass of a simple ppzxp/g 7:px* pendulum is tripled, the time required for one complete vibrap/7 zpx:p p*xgtion

  Both pendulum A and B are 3.0 m long.1ylc( q;m xd: hzh mhrw4t.; eog(0k+v9tq5gy The period of A is T. Pendulum A is twice as heavy ty q(l +5o(mh:kh;xcdyhw9e0q 4 m1.;zrvt ggas pendulum B. What is the period of B?

  When the length of a simple pendulum is tripled, the time for one complete vibra +x yk: )kl8s4pv9k+kt)l tapltion increases by ayk +kas:pxpl t)4lt k +)lk98v factor of

  What happens to a simple pendulum's frequency if both i1m wtir/+w d.tts length and mass are increased?t rw tm/i+.wd1

  Simple pendulum A swings back and forth at twice the frequency of simple pend5/2v ydtr o(akulum B. Which stateodkv5a(/try2 ment is correct?

  If you take a given pendulum to the Moon, where the accelerati:ibx+r) ce id1u gn8n.on of gravity is less than on Earth, the resonant frequence+cubn8:i1)d .ig nrxy of the pendulum will

  Curve A in Fig. 11-1 represents )673ms5qkksq+r b-z0r ahuwp

  Curve B in Fig. 11-1 representp vcl-.)hgqu*+7un ep s

  Curve C in Fig. 11-1 re)k nlwc 7w0w;hpresents

  For a forced vibration, the amplitude of vibration is found to depend on thq 9gs-1qgsh qgg7 e--je

  In a wave, the maximum displacement o i)d /c mf06q(uipprl,f points of the wave from equilibrium is calirc,/p i)fmqd6 u0(lp led the wave's

  The distance between successivep3o0 wl qy)(cj crests on a wave is called the wave's

  The number of crests of a wave passigc ;6k/0xvkffmyp/3vng a point per unit time is called the wave'sfykx k6mfvp03;g //cv

  For a wave, the frequency65 e6pe:3/1mzvzzkw pdlkyq7 times the wavelength is the wave's

  The frequency of a wave increases. Whq .. ruca9)f0gp:iq cbat happens to the distance between successive crests if the speed remains griqc0b . cauq)9f :p.constant?

  A wave moves on a string with wavelengtiq0aa ljc)p: 2h l and frequency f. A second wave on the same string has wavelength 2l and travels with the same velocity. What is the frequ ql)a:2a jic0pency of the second wave?

  Consider a traveling wave on a string of length L, mass M, joc,5v:phy4w8hgm h3x,) kmw and tension T. A standing wave is set3j8wk g ,hm,y 5c)h4vmwohxp: up. Which of the following is true?

  A string of mass m and length L is under tension Tqi6g6o)0e4- i ct rltm.2id7w;f yos g. The speed of a wave in the string is oo6li qdmg iswr- yc.)egi 0f2;7t4t6v. What will be the speed of a wave in the string 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 i88px;, ft)af3nsojktension T. The speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L, with no onpikaf,f )8 38st ;xjchange in mass?

  A string of mass m and length L is under tension T. The speed of a wa) lu2bvo58:bjrn r 7o bdt3qt ue6:(mive in the strq3m6( do vt7r::) lbrbbtu8oe iunj25ing is v. What will be the speed of a wave in the string if the tension is increased to 2T?

  In seismology, the S wave is a transverse wwzv)q 1d)*o,bv/osdn(; fpqjave. As an S wave travels through the Earth, the relative motion between the S wo1f *qj)nb,/svp)z d o;dqv(wave and the particles is

  In seismology, the P wave is a longitudinal wave. As a Pmj05+mjc w a1l wave travels through the Earth, the relative motion between the P wave and the particles cjj +5ma1mlw0is

  The intensity of a wave i 8:oyf bb;xto.s

  A wave pulse traveling to the right along a thin cord reaches a discontigp9j(k vqnm(p(l/jz 0nuity where thp(z jl/ k(nq0mv9gjp( e rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

  Two wave pulses with equal positive amplil,*y7 w( awnq4kyh1tttudes pass each other on a string, one is traveling toward the right and the other toward the left. At the point that they occupy the same region of space at the st1 y h,4yqn7(al* wwktame time

  Two wave pulses pass each other on a string. The one w0j*u5 erv lf2c ec:uy*lub//d - be:atraveling toward the right has a positive amplitude, while the one traveling toward the left has an equal ampl bud cewea/* b:l0rl2j-vuy f/c*u5:eitude in the negative direction. At the point that they occupy the same region of space at the same time

  Resonance in a system, such t ln 07ig)*sx p,jryoihfw 50,mez2g03v3kpu as a string fixed at both ends, occurs when

  If one doubles the tension in a violin q2v4ud r1-nh c9/saj rstring, the fundamental frequency of that string will increase9a qrhjsv14u2 dc/n- r by a factor of

  What is the spring constant of a spring that stretches 2.00eam c u*zo )t(g; hdl(kzr(/y) cm when a mass of 0.600 kg is suspended frortyzak)/) mdl(egz c(u h(*o;m it?

  A mass is attached to a spriek5n6n/ub/j.z 4 ulvbng of spring constant 60 N/m along a horizontal, 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 equilibrib /.en654n kb/uvujzlum position when it is oscillating. What is the amplitude?

  A mass is attached to a spring of spring constant 60 N/m along a horizontaj9jeg8q9;49j o wgeyo u v/n rycp*c23l, frictionless surface. The c goeevn;r3jj/wo9gc 9q * p8u y9j4y2spring 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 horizontal, fdgs,3s:pxtn6 2 i4y *mc ba;t,z0eeiy rictio :g4e,ss zdt icax0ypy,;e3 b ni2mt*6nless 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 frequency of oscillation?

  A mass on a spring undergoes :.m t6roh; wi.oezb.l +(fdx tSHM. It goes through 10 complete oscillations in 5.0 s. What is the pert d..o6+hb :iwxet f(rl.; zomiod?

  A mass vibrates back and forth from the free wta 7hl+:a,b g7ixe6,ezlot xgg4.p, end of an ideal spring of spring constant 20 N/m with an amplitude of 0. 7e ,7gezo pt6gagbt ,hxax.4+li :lw,30 m. What is the kinetic energy of this vibrating mass when it is 0.30 m from its equilibrium position?

  A 0.50-kg mass is attached to a spring of spring constant 20 N/m a;qhm2e( k cqp.long a horizontal, 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 2p kq hq;(e.mcthe system?

  A mass undergoes SHM with amplitude of 4 cm. The energy is 8.0 J at this time26e1y 4eg egr(/8k x ngog(fvq. The mass is cut in half, and the system is again set ig/g e(o(68x gkfrqv2 e 1geyn4n motion with 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 20 N/m along a horiz dgy -h/.irr,i(pced+ontal, frictionless surface. The objectgyc i+hir, edp-/.dr( oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What is the amplitude of vibration?

  A 0.50-kg mass is attached to a sp4ncnu)j fm4 i3ring of spring constant 20 N/m along a 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 locati4fu3cij4mn ) non are the kinetic energy and the potential energy the same?

  A 2.0-kg mass is attached to the end of a horizontal spring of springie+y4pefw(nmd1 yqca 5 -gi4 * constant 50 N/m and set into simple harmonic motion with an amplitude of 0.10 m. What is the total mechanical energy of thisp+cwg-e*y 4qin15fam (i 4yed system?

  A 2.0-kg mass is attached to the end of a horizontal spring of spring constan;ntyj dc13 e-dt 50 N/m and set into simple harmonic motion with an amplitu;- 13jndte dcyde of 0.10 m. What is the total mechanical energy of this system?

  A mass vibrates back and forth from the free end of an ideal spring of sprik6.xxuip0 xs1gsx+.p ng constant 2.ip6p0.+ux xsxg1sxk0.0 N/m with an amplitude of 0.250 m. What is the maximum kinetic energy of this vibrating mass?

  The mass of a mass-and-spring system is displaced 10 cm from its equilibe *sz aw bfeme9ym7kf c ),fxi21g)9-irium position and released. A frequency of 4.0 Hz is observed. What frequi e919g,xe*w) si zycaef-mf m7)bf2kency would be observed if the mass had been displaced only 5.0 cm and then released?

  A 4.0-kg object is a3 ./nkvk x1 bobm.w--ec f-pebttached to a spring of spring constant 10 N/m. The object i-pbv1o ef e3/b ncxb-k.w.mk-s displaced 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 spring constant 10 o+s n;mfj oyn5 o 8b;qc+jm,;nN/m. The object is d;o;,+nnc5bmy mf8j osn;j qo+isplaced 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 of spring constant 18 N/m, dikwc v6 ) pd20jkb)2dl x* iwq5dtf3kguxlo56 3splaced slightlyq dg ckou6kd tp 0k*x5f 362wwld5)vlxb32ij) from its equilibrium position, and released. What is the frequency of its vibration?

  A mass is attached to a spring. It oscillates at a frequency of 1.27 (ozlp o 4:l(0gbx.fy);ltnpd;1phxx/yw p j9Hz when displaced a distance of 2.0 cm from equilibr1 l g;(l t0xfpx.obx yp)zjo4wp;9ln: pd( h/yium and released. What is the maximum velocity attained by the mass?

  Two masses, A and B, are attached to different springs. Mass A vibrates with 4vw)jb3 ts e6pamplitude of 8.0 cm at a frequency of 10 Hz and mass B vibra6e tbvp)4 wj3stes with amplitude of 5.0 cm at a frequency of 16 Hz. How does the maximum speed of A compare to the maximum speed of B?

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches the31 6l 7 -b)dx9 dbhfiye wr5y9t*vjwxw spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Calculate the period of oscillation7vb)9h *y-jwi 1d9lyxwrdx 56ftbwe3.

  A 0.30-kg mass is suspended on a spring. In equilibriumth 7y9r37pba s9e0xck the mass stretches the spring 2.0 cm downward. The mass is then pulled an addition ckey 09bhr aspx797t3al 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 sprine (kl6ho,+ tvjb ;j6(lrts/bp g. In equilibrium 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 resvrpklh btj,; (6s b6lj /(eto+t. Write down its equation of motion.

  An object in simple harmonic motion obeys the following position v4.r h :qo6yk ha+skz6gna;.j-b2qlhversus time equatioq6kh6 .- .n hza;ary2vj:lqog+ 4 hskbn:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple har2 ;gme d3orfn6l 19khbmonic motion obeys the following position versus time equn9o1;3fr2bk g6h ld meation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following position versus timebsrt80/ w z:uo equation:ru wzob:8/t 0s
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the f*2s hz mklb) wi5.ws.+o+uph q2phof8ree end of a spring executes simple harmonic motion according to the equation. sbhw)l ko.8 5+quh*m2wp+sizp2hfo $y = 0.50 \; \sin (18\pi \times t)$ where y is in meters and t is seconds. What is the period of vibration?

A 1.5-kg mass attached to spring with a force constant of 20.0.3 f4voh pon,q N/m oscillates on a horizontal, frictipqon,v3f 4h.oonless 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.)
(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. d,ar(l, czvlnot90)s -z+rmlk6l- mk(a) What are its frequency and period on r ktm+ko,r()6-dc-9lms, vlz al0z nl Earth?

  A 3.00-kg pendulum is 28.84 m lon4stgm 0 jtc,0sg. What is its period on Earth?

  A pendulum has a period of 2.0 s on Earth. What is itsq/uz 4cs31;u3 mu qsk x(pslimb;1 t;p length?

  The pendulum of a grandfather clock is 1.0 ma,3u t cgv)eo1 long. What is its period on the Earthgeo3va ,)tu1 c?

  The pendulum of a grandfather clock is 1.0 m long. What is its period on t fgsr -1c8av)u7j2xwehe Moonejgv)8 rcs-7wuf 2x1a where the acceleration due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-kg sphericalfp 6.h-xmgzwt*lm 5 6z mass attached to a massless string. When the mass is displaced slightly 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 z- *.6mx mgtw6fzp 5hlattached to the string instead?

A simple pendulum consisting of a 20-g mass has initial angular diyu fhkmf+3a *o+n hd.6splacement of 8.0e. It oscillatehf+ n6.myu dh*+f oa3ks with a period of 3.00 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 cfpi e13k(u g5s:9v i- nsw67lx(bvjctime. The frequency of the wave is 120 Hz. What is the amp :(gknvi75x( svwfjeccbi 3 -1s96luplitude?

  Figure 11-2 is a "snapshot" of a wave at a given time. The f9 l 0r0bd wqvh8a8gdhso1,;su tx o7l*requency of the wave is 120 Hz. Wlt ,saw0lo rdv0q u91bsh*x 8o7dhg8; hat is the wavelength?

  Figure 11-2 is a "snapshot" of ad ,+6 o awl*jy;dlys1bq8efxt,p9*ck(tv qe1 wave at a given time. The frequency of the wave is 120 Hz. What is the wave xp; bd*1alcwqo skyf(e d q96te,tjv8y 1+l*, speed?

  What is the frequencxt7+fl- ze gnr2j;b3lfd 6vm5)uw:wa y of a wave which has a period of 6.00 ms?

  What is the period of a wavetwfz, w89;e2xnj;pv ;rgzk dsi1xlwb1w-y:8 with a frequency of 1500 Hz?

  What is the wave speed if a wave has a frequency of 12 Hz and a wavelength j725eppfylz )q7nlrk rl +0.zof 3.0 m?zf.ke0 pnl )7z +2l5 pyjrlrq7

  What is the velocity of a wave that has a wavelength of 3.0-(am-j pu6poepw 7;ls m and a frequency of 6 ;u7j(s- mape-ppwol 12 Hz?

  What is the frequency ain 7xbw1;o7k2nz gw qjgm1r)k,/ hr.of a 2.5 m wave traveling at 1400 m/s?

  A piano string of linear mass density 0.0050 kg/m is under a tension of 1350 Nla1r6ten4;mr9 0 l6 9oai atis. What is the wavear0oet4 rt 1 al9ai;s li66nm9 speed?

  A string of linear density 6.0 g/m is under a tension of 180 N.xvmh*ptbs* , ,8;ehs e What is the velocity of propagation of transverse wavextvh se,,sp;8*eb*mhs along the string?

A wave whose wavelength is 0.500 m is trihr9tsuc/ crx,.(bo vu(* n7 baveling down a 500 m long wire whose tota. xru(un*/r7hsc 9t i(bvoc b,l mass 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 propag*g9ka i fwf+f)ation of a transverse wave on a 2.0-m long string fixed at both ends is 200 afi*f f)k+gw9 m/s. Which one of the following is not a resonant frequency of this string?

  If a guitar string has a fundamental frequency of 500 Hz, whic+z4k.x rfq+i+4 s rqpbh one of the following frequencies can set the string into resonant vibratr zqp bs +if+k.4+qr4xion?

  A stretched string is observed tof ez p368tkr9c have four equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wave w pz6e8 3ktfrc9ith five equal segments?

  A string, fixed at both*xb mjm:x-hv1r l8+uw ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops. What frequency is needed if the standing wave ph lrw8 * +bvu1jmxm-x:attern is to contain 4 loops?

  A string of linear density 1.5 g/m is under a tensionq)1cyp-p8fds -i 0j rv of 20 N. What should its length be if its fund1j0r-8-qfvcp sp i)yd amental resonance frequency is 220 Hz?

  Find the first three harmr+zdu 5:ge zj/ jsgya9x( q(sfvo+;g;onics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjezxgvaj( g :(z;+ ;os qyjf9rg5ud +/sected to tension of 50.0 N.

A string of length 2.5 m is fixed at both ends. When the string vib 58ru kh, xdah2*5cbqhrates at a frequency of 85 Hz, a standing2q 8ha5,dux* hc5 rkhb wave 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.