The time for one cycle of a periodic process is cao9(v+apn(wlv1n8u/op6eyh (keus g 4lled the

  For a periodic process, the number oxofg, 5d4u(mwf cycles per unit time is called the

  For vibrational motion, the maximum displacement from the equ4 ptw/vqd +bu.ilibrium point is called td+uptv4 /b w.qhe

  A mass on a spring undergoes SHM. When the mass is at its wex4wqtx5kx8h2 ;r;lmaximum displacement from equilibrium, its instantaneous ve x5 ;ext8h4r2k ;wwxlqlocity

  A mass on a spring uu 8z0h18c ds9lpw1 cdyndergoes SHM. When the mass passes through the equilibrium position, its instantaneousdl zcdy8s1c98 uh 1wp0 velocity

  A mass on a spring undergoes .wn-p i;,*xm kgbvju.0rrmvg-(c+ o qSHM. When the mass is at maximum displacement from equilibrium, its instapgv( ,r0 uvw jco.r-+;b mnximg.q-k* ntaneous acceleration

  A mass is attached to a vertical 7jq(zne e pk;xsyzf 1t))s+-ispring and bobs up and down between points A and B. Wk)qz y i1esj -e+sfz 7n(xt;)phere is the mass located when its kinetic energy is a minimum?

  A mass is attached to a vertical spring and bobs up aw1 vbwkbvi.a. n.ng+0q gsf+:nd down between points A and B. Where is the mass located when its kinetic energy is a :1b.vsivqnf+b+ k .n ag.0wwg maximum?

  A mass is attached to a vertical spring and bobs up and down between pw fx3ozn6eq6hjhol nq xf.4q4 3ww16- oints A and B. Wher xnq 3z h 4howf-q3j4wq6e1xo.lfwn6 6e is the mass located when its potential energy is a minimum?

  A mass is attached to a verticalzj1-7,fs j3b wz;fzj4 mned9q spring and bobs up and down between points A and B. Where is the mass located when its potentizffm zjb9ewq-1,7 ;4jns3zdj al energy is a maximum?

  Doubling only the amplitude of a vibrating mass-and-spring b-srci b5 co)y+/k3h4u xoko*system produces what effect on the system's ucooi s)y /4ro3b+k-ch 5x*b kmechanical energy?

  Doubling only the mass o1+wppf / g2ycvf a vibrating mass-and-spring system produces what effect on the system's mechanica /w2v1ypcg+fpl energy?

  Doubling only the spring constant of a vib j) 2vmn;vpaw301 uxoqrating mass-and-spring system produces what effect on)a pw30 jvxm;2o1 nuvq the system's mechanical energy?

  A mass oscillates on the 0u ehj8ys:r4r; so6 b,w:amis end of a spring, both on Earth and on the Moon. Where is the 6ebm :j sh:;,r4s8asi0yow u rperiod the greatest?

  Increasing the spring constant k of a mass-g osip r.a,b-zsost62 9+8xzcand-spring system causes what kind of change in the resonant frequency of the system? (Assume no change ipzo-2ags, 9rbxt.z+ 6s8oc si n the system's mass m.)

  Increasing the mass M of kzdkxc8uez: lvr *w( t4(-g:ca mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the system's spring consetz (uk:gd vw( krz*c4-lc: 8xtant k.)

  Increasing the amplitude of a mass-and-spring system causes what kiwv7w w2j9yh.o6p e:( n2yqawund of change in the resonant frequency of the system? (Assump(:e uhqno7jww92aww2.6yy ve 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 ma : +)rt-ppee4a jw9i kos(mtm-ss M attached to a weightless string of length L. For this system, when unap)kt-ie4 m -ow(pstmr9j:+ edergoing small oscillations

  When the mass of a simple pendulums sjw8n/62z mnw 5u3 h(-xlr;rxe1se l is tripled, the time required for one completenrl r lx e(3 sm56jeu;wwnhs1-2zx/s8 vibration

  Both pendulum A and B are 3.0 mv4mgug4. bul )4bv u/g long. The period of A is T. Pendulum A is twice as b/l).g4mvuu44ggv ubheavy as pendulum B. What is the period of B?

  When the length of a simple pendulum is tripled, the time for )7tma 43czy: fzrps5w j-keg,one complete vibration 3k sm-rae,:7wtp)cz4z5 y gjfincreases by a factor of

  What happens to a simple pendulum's frequency if b3p r2yv uu,9mmoth its length and mass are incre3,pruvmyu 2 9mased?

  Simple pendulum A swings back and forth at twice 3)-oig 3 h7kf4 iezkcfkssx6- the frequency of simple pendulum B. Whicif3 e s74z 6k)ks-o3fxc-kih gh statement is correct?

  If you take a given pendulum to the Moon, where qm:4o 2piijs5xnft.f+9m( *taq.v gxthe acceleration of gravity is less than on Earth, the g+m.qxqt:p jtxs.2i5 f 4ia*m9f( nvo resonant frequency of the pendulum will

  Curve A in Fig. 11-1 rzh;zk6rt a plhubv*5 y7 e-/g1epresents

  Curve B in Fig. 11-1 represej(v9k.f -fmc6al zqb4xrh:-q .gx3vc nts

  Curve C in Fig. 11-1 ry 7 fd5m2y50eiwseu q+epresents

  For a forced vibration, the amplitude of vibration is found to d-5yqsi3 sta q vlj:,m8epend on the

  In a wave, the maximum displacement of points of the wave from equilibrium wh 7ddiy i6k-gq.y4m9is called the wavidyyi7h9mg 64kd q-w.e's

  The distance between successive crests on a wave is called the wai 61oqln vr) :6c 5dhxx2kyyg*ve's

  The number of crests wloumw-spl/56t8f1 e of a wave passing a point per unit time is called the wave's 5wl8 ps/tw1o-ue m6lf

  For a wave, the frequencyeg,*7a/ izzahy60vpi times the wavelength is the wave's

  The frequency of a wave increases. What hapdtim9d8; ai4p)p paa3 pens to the distance between successive crests if the spi )m4adpadt93pp i;a 8eed remains constant?

  A wave moves on a string with wavelength l and f 2*p+ 3fiu*fdy ;hr ,ptndv6otrequency f. A second wave on the same string has wavelength 2l and travels with the same velocity. t pft h uf,d6vroi3+y*pn;2 d*What is the frequency of the second wave?

  Consider a traveling wave on a string of length L, masso6 f e.7k, tn1:nd(bvgr vu zig0mb)3g M, and tension T. A standing wave is set up. Which of the f6.3buvb0negtk,7gf o gi:(mnvz1d ) rollowing is true?

  A string of mass m and length L is under tension T. The speed 32n0 ig;fsf-wnny d3nof a wave in the string is v. What wifn32;n fn3w-g ys0dn ill 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 tension T. The speed of a wave in the s0 w5io6ggpxe3 ;hf q wq6me.6string is v. What will be the speed of a wave in the string if the length is increased to 2L, with ni6ehw6sp5xe06g omf3 ;g qwq. o change in mass?

  A string of mass m and length L is under tensc me s*2nax8ig1xh5 (kion T. The speed of a wave in the string is v. What will be the speed of a wave in the nxg8seha(5x 1mci*2 kstring if the tension is increased to 2T?

  In seismology, the S wave is a transverse wave. f;ixa/f v wn0yzwi2huk*l+q/s);c2p As an S wave travels through the Earth, the relative * wlf h ny)+2uipxwi/;svc; 2qfkz/0amotion between the S wave and the particles is

  In seismology, the P wave is a longitudinal wave. As a u6i8yh+ f+it-kzgx k5lw 0a.:k*fdbj P wave travels through the Earth, the relativa j.:x g+fud8blyz6h0fkit+w 5 *k-ike motion between the P wave and the particles is

  The intensity of a wave y: mkm.oi5fo3 biws1g*kvl3r+ lv (l.is

  A wave pulse traveling to the right along a thin cord reachzrpyi nw55job , 9c6/n op6xa*es a discontinuity where the rope becomes thicker and heavier. pz 5 o/opi96n5x 6bc*ynwaj r, What is the orientation of the reflected and transmitted pulses?

  Two wave pulses with equal pwdpp uyat+:/ nh9d fu0 f0)0ibzk),q4ye et.yositive amplitudes pass each other on a string, one is traveling toward the right and the other toward the left. Ayyb)t p004 y)k/9+de.upe itwd nqhffa 0,u:zt the point that they occupy the same region of space at the same time

  Two wave pulses pass each other on a string. The one traveling toward the r,kk(- jdj1d* )laexla vlr)m)j*mgb)ight 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 l1)d ka j*) -xd*e(j,al )vgbl k)mrjmsame region of space at the same time

  Resonance in a system, such as a stja6o k0/y.qjsks7 e d k4v87hdring fixed at both ends, occurs when

  If one doubles the tension in a violin string, the fundamental fre/k2t q g 7z*(rkwl-sirquency of that string will in*i (rq/7z-tls2kk wrgcrease by a factor of

  What is the spring constant of a spring that stretches 2.ut+fmg2ujj-pco 6- krq) 5r 6x00 cm when a mass of 0.600 kg is m c6+5urk-gp ofxtu-6 )jjrq2 suspended from it?

  A mass is attached to a spring of spring constant 60 N/m along a horizontal, filoyq uevn2oz -50;d;1c g*2w uwk qj8rictionless 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 posi;duq2e;ujok-1 *cnw8o 0vy5z2i l wqg tion when it is oscillating. What is the amplitude?

  A mass is attached to a spring of spring 424l)nagx 7k okcom 6kconstant 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 equilibrium position when it is osci6ck4oa k2)m loxg74n kllating. What is the period of oscillation?

  A mass is attached to a spring of spring constant 60 N/m along a br /0,2txxfswb,4 qtv horizontal, frictionless surface. The sprinbqbx,w42r/s ,ttv0 x fg 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 SHMv7ul e -ihwb*7y tvy.2. It goes through 10 complete oscillations in 5.0 s. What is thy. 7t7ubhivev2wl*- y e period?

  A mass vibrates back and forth from the free end of an idebd7syc mk*kal hh ,)07al 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 0.30 m from itsabdh)0 7lc k,7* mkhsy equilibrium position?

  A 0.50-kg mass is attached to a sprjqq9r92q-()mjfvg x+tduzr*y:t,+ ,ttcs sj ing 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 equi+ +tjdq992t)q ,j uc-sqv j r*t:ygmf(s,ztx rlibrium position. What is the total energy of the system?

  A mass undergoes SHM with amplitude of 4 cm. The energyql zd)x)j x;x54s8 nxi is 8.0 J at this time. The mass is cut in halfxxn4 ; z5li)dsqxx)8j, and the system is again set in motion with amplitude 4.0 cm. What is the energy of the system now?

  A 0.50-kg mass is att ttcf0-t)4o lhached to a spring 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. What is the amplitude of vctt0) -tolfh4 ibration?

  A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizona-:m-lb*i,,qq xzvc,bn * zydtal, 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 energ zx:a,-dqbzyc, v*q *bnm-il,y and the potential energy the same?

  A 2.0-kg mass is attached to the end of a (6 z2mlyj; th1t 5ee5*eloc*wdp)ug ohorizontal spring of spring constant 50 N/m1t26e; twodc5e*e5luz (gl)ypmjh *o and set into simple harmonic motion with an amplitude of 0.10 m. What is the total mechanical energy of this system?

  A 2.0-kg mass is attached to the;ncscuj r7/0r5ke8/1j i *un6w wsju z end of a horizontal spring of spring constant 50 N/m anj 5su6 /e*j1snu7j 0wi rw8nzkucrc ;/d set into simple harmonic motion with an amplitude 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 ideb;;1 pp fiotf+pphpkkgap+-) x f4*s.0s; ma sal spring of spring con sg+xmp4;+p;;ia)b fhp.o fspfp kkt a* s0-p1stant 20.0 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-spzev3fkfe,.: +8l8v uhonl 5djring system is displaced 10 cm from its equilibrium position and released. A frequency of 4.0 z8jen5 ud+,.v f 3v8ehk:lfolHz 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 coi+ qxhcw3b.9tnstant 10 N/m. The object is d9 iqwtb +cx.3hisplaced 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 luoro(): m han d0;j6wof spring constant 10 N/m. The object is displjh:u)dm(nrol ; aw6o0 aced 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 9ld74qna ;zeck ec (-sof spring constant 18 N/m, displaced slightly from its equilibrium position, and 4zsee(a-lnq ;k 97 cdcreleased. What is the frequency of its vibration?

  A mass is attached to a spring. It oscillates ad9 rt u6,l,8 pk6te,dngwt(ont a frequency of 1.27 Hz when displaced a distance of 28t r ,t9p6d,knoeg (unt6w ,ld.0 cm from equilibrium and released. What is the maximum velocity attained by the mass?

  Two masses, A and B, are att)5 nk s8xb3lr4,1j eed lk+nahs.*hd yached to different springs. Mass A vibrates with amplitude of 8.0 cm at a frequency of 10 Hz and .5l4ne,dln shh s1 *3x+ bkyadk)r8jemass B vibrates 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 odh)y3g nqy/)p1 w c,lequilibrium 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 t olgwd/c3)1nqy)ph, y he period of oscillation.

  A 0.30-kg mass is suspende,cyw2jz g3xy+lga5 5 vd on a spring. 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 r3y2 +5vzwj5glxg,yac est. Calculate the total energy of the system.

  A 0.30-kg mass is suspended on a spring. In equilibrium tthp12k (smv raj;m-r3he mass stretches the spring hkapm132 rr -;svmt(j 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Write down its equation of motion.

  An object in simple h2 s(xfy,k;rw2n neac8 armonic motion obeys the following position versus time equati2e(kx ,n 8f2scrna yw;on:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the following prmyp-n+sw53+nx s gp :r be3tr8vh60gosition versus time equatiomntsb-ex:hgv3568rp0 +pgnr+ 3rsy w n:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following position versus time euet-u34 * yf,lbjwx c3quati cyjetu 3-4*xbu,w3flon:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes simple harmonic motion accor1 rw h ,b5qo3jqt+0i 5tku9rirding 3orbrt+i,hwu0qrq15k 5i 9jt to 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 spring with a fow fje.rzciax/ xp:); 6rce 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 .fer:;wx6 c /pxijaz) 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. (a) What arwupfu+xx4f) t3-t .lk neyc sy.r8*o+l-5 a uje its frequency and period on Earanfl3 x)- cyprf5k +uu.-*.eo wl s+x8tt4jyuth?

  A 3.00-kg pendulum is 28.84 m long. What is its period on Eudvg5x cr:q stfkgls ;u,1r8-h ii3,7arth?

  A pendulum has a period of 2.0 s on Earth. What is its l01zk ,i5 )ckabgv38h2g llh blength?

  The pendulum of a grandfather clock is 1.0 m long. What ;*wuog21xd xyh1hbi ;is its period on the Eax* d;12gxho ybw1hi u;rth?

  The pendulum of a grandfather clock iso4*9rvg0cc 5gk 9vrtw 1.0 m long. What is its period on the Moon where the accelerag0c59*v rtv c 4k9wogrtion due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists w1 ki:fq(:qoyf,, febof a 0.25-kg spherical mass attached to a massless string. When the mass is displaced slightly from its equilibrium position and released, the pendulum swings back and for y( qk ,fo,eibq1ff::wth 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 hak zdis k t6,upto93)0ns initial angular displacement of 8.0e. It oscillates with a period of 3.n), ktp6d tio z0k93us00 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.jv,ku1nfhxx o+630o r The frequency of the wave is 12uv3+k 6nj0 ,xhfoorx1 0 Hz. What is the amplitude?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frequenc4t rk lc(qm)w6y of the wave is 120 Hz. What is the wave4r k( )mtqclw6length?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frequency of the5xgo b*zdb4psuhq+; rm b, 4(y1t ue(y wave is 120 Hz. What is the wave m, he1( d 4xuys(pby;g5b+b uzt4r* qospeed?

  What is the frequency of a wave which has a period of 6.0e ht6.v3kk:zc owilb h.fin-6 j)7qy-0 ms?

  What is the period of a wave with a frequency of 1500ri4:l w7 go /pk* lewn7-xvlu6 Hz?

  What is the wave speet 3f/dy.opono2pn/. m7(dtied if a wave has a frequency of 12 Hz and a wavelength of 3.0 md.p/2ym(3it.td/ neo 7n poof?

  What is the velocity of a wave that has a wavelength of 3.0 xjzz)tw0bu( 1 m and a frequency of 1 )j0uw(btxzz 12 Hz?

  What is the frequency of a 2.5 m ww i9ox1 u/a 56ijg5 dlv*f7kpfave traveling at 1400 m/s?

  A piano string of linear masdjd4*rw6cu tje 5 y/ /()k0bwdqgzog*s density 0.0050 kg/m is under a tension of 1350 N. What is the wave speed/ww* ) e*j (gguddt b4c06ojryz/5kqd?

  A string of linear density 6.0 g/m is under a tension of 180 N. What is *c)s l6o).svmr ,.kkgc gpe9w the velocity of prop6 l..c,)rwspk *)esc9 mkvggo agation of transverse waves along the string?

A wave whose wavelength i;kl2eibq:7 cv s 0.500 m is traveling down a 500 m long wire whose totav 2eckq7lib :;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 propagation of a transverse wave o2l4nf sj 6.eqan a 2.0-m long string fixed at both ends is 200 m/s. Which o4f.en alj2s 6qne of the following is not a resonant frequency of this string?

  If a guitar string has a fundamental frequency of 500 Hz, which o(7u s :-ery6f0nqst ro.8swmyne of the following frequencies can set the string irs -7f0uysetny:w (o 8.q smr6nto resonant vibration?

  A stretched string is observed to have four equal segments in a staml,n.z7sxp sdt e3(/vnding wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wave with five equal segmentsm 7ed.zn ,s 3spt(lxv/?

  A string, fixed at both ax,3c5u8f: y xg vs:xsi8e+yc ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops. What frequency is needed ycfx,: c+:s us38axie5g8yx v if the standing wave pattern is to contain 4 loops?

  A string of linear density 1.5 gq2e0 n*4spppd /m is under a tension of 20 N. What should its length be if its fundamental reson 20qp4n*psdep ance frequency is 220 Hz?

  Find the first three eoxv3o1(d5 cxb6xt j6harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tensionx61b( vtx 6oj o53ecxd of 50.0 N.

A string of length 2.5 m is fixed a*egsaped.uo3hfg ::ev4w s3)b2s x* zt both ends. When the string vibrates at a frequency of 85 Hz, a standing wave withv:3 ss hw42.gog:epf zxabd)u3 s*ee* 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.