The time for one cycle of a periodic process is ckc : e(xc3xl qu,7em-+ghoe.v t.hyk, alled the

  For a periodic process, the number of cy e42ymy(.njrn e8 profp)60 tmcles per unit time is called the

  For vibrational motion, the maximum displacement from the equilibrium pointa vnpeiuo*l w c6-9y:u+:h0m u is calll:avin*uym6:- 0wu po+h e9uced the

  A mass on a spring undergoes SHM. When the mass (wp*v;s p2 kybis at its maximum displacement from equilibrium, its in;*psb w2vpyk(stantaneous velocity

  A mass on a spring undergoes SHM. When the mass passes through the equili 5* 70dhzqaszva1o (febrium position, its instantaneous velocfzh 0qadz1se(7 ov a*5ity

  A mass on a spring undergoes SHM. When the mass is at maximum displacement froml5 ,qelo +unf j,6e*co equilibrium, its instl*+j,qeloo 6f,5 ceu nantaneous acceleration

  A mass is attached to a vertical spring and bobs up and down between n3x/4n tlk-fypoints A and B. Where n-y/nx3 klf4tis the mass located when its kinetic energy is a minimum?

  A mass is attached to a vertical spring and bobs up and down between points Awl0dfdrq mby4 9 .pt9, and B. Whererp,0t.4qd f y9m b9wdl is the mass located when its kinetic energy is a maximum?

  A mass is attached to a vertical spring agvm v dxb, (vk.d6a5ei4; p5gpnd bobs up and down between points A and B. Where is the mass located5x ;.padmgb(4,kv65ep v v gid when its potential energy is a minimum?

  A mass is attached to a vertical spring and bobs up and down betwifcp)rnf-1fuj 9 z 8+zb;h g3geen points A and B. Where is the mass located when its potential energy is au gcfh+zff-b1)rinz 9j 3p; 8g maximum?

  Doubling only the amplitude of a vibran0d rbhwvn(u;,t s4 .k;*+jszzoyw+q ting mass-and-spring system produces what effect on the s wdwq 0nos+ tb(v.y+;s,hnr;4zuzk*j ystem's mechanical energy?

  Doubling only the mass of a vibrazn8bjczbo +w3 7*.aejting mass-and-spring system produces what effec jc7a zeoj. wbz3b8*n+t on the system's mechanical energy?

  Doubling only the spring constant of a vibrating mass-and-spring syutzxi1y()qn0 w1/xtnd96ax -* hh ajmstem produces what effect on the system's mechwm/ z ) 9xhhjatxt1n x6yn0d(qa*1-iuanical energy?

  A mass oscillates on the end of a spring, both on Earth and on the Moon7l lwjd +8xev*fx*s6 u2p 0+1ljkjmkj. Where is the period thes67e jf1mx j +*l82xj0lp+dw k vukl*j greatest?

  Increasing the spring constant k of a mass-8ssc 1 lxt c+2,gocc ulig0u(6and-spring system causes what kind of change in the resoncg l8,su6ogls 01+cccx2 ( tuiant frequency of the system? (Assume no change in the system's mass m.)

  Increasing the mass M of a mass-and; 8jha;fcqyf i28m jl8-spring system causes what kind of change in the resonant frequency of the system? (Assy f;8c2 la8fhj;8qijmume no change in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spring systdp:gij s,(r6jgi +ezb7zj2 kd*:ny2sem causes what kind of change in the reb*sz:s g7j :i2jejky 6pn,r (2+ gzdidsonant frequency 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 mass M attached to6 :4dnp;jewnw a weightless string of length L. For this system, whe6e 4;:dpnw njwn undergoing small oscillations

  When the mass of a simple pendulum i7 vawq;dn rvw 9ck,4*xs tripled, the time required for one complete vibration 4 v9vqr*xwakd 7;wcn,

  Both pendulum A and B are 3.0 m long. The period of A is T. Pend*kme,ugsa +r +ulum A is twice as heavy as pendulum B. What is the perio ek+,+mga *usrd of B?

  When the length of a simple pendulum is trid1:h o-xc n6ispled, the time for one complete vibration incr1n-s: hx 6coideases by a factor of

  What happens to a simple pendulum's frequency if both its length and7u k cy,roi* gqjc -e+e0u9bt/ mass are increaeb g-rc9ikquye *t70+, c/ ojused?

  Simple pendulum A swings back and forth zzh6 h61-( ,xkgz ;xp a/3k6ogn vspdmat twice the frequency of simple pendulum B. Which statementh;odg,3x 1z(ak6 n p sgzhxpzv 6/-m6k is correct?

  If you take a given pendulum to t: f.wm9kfive06sk zgb- wv8-x/k nsm/ he Moon, where the acceleration of gravity is less 9-.8/w-0 sm/bwzkx6 vnk:gm s e ffkvithan on Earth, the resonant frequency of the pendulum will

  Curve A in Fig. 11-1 repkoio u01)o-nxkdr9o ,resents

  Curve B in Fig. 11-1 repr sd7f wxi zix l+ 77est)3wwdvv.rv,,7esents

  Curve C in Fig. 11-1 represe4.aj peg,2*9hboylj c1 lk7 gunts

  For a forced vibration, the amplitude of vibration i1hf01 t d6kx8t)zb qzvvkuo23s found to depend on the

  In a wave, the maximum displaceme:orh446qng f/; whynp nt of points of the wave from equilibrium is called the wave's; y4 fwnphnorg:64 qh/

  The distance between succe*ng ecgspy9;* ssive crests on a wave is called the wave's

  The number of crests of a wave passing a point per uni/5e y)6cpyxetn.q2 b pt time is called the wave's5/ by x6p2qtee)pnyc.

  For a wave, the frequency times the wavelengtw6ciwu5 1vk,c,:vzy 4a(3 :aeogjzmyh is the wave's

  The frequency of a wave increa p6,o: dt(okk5 0.fj9 am9pbfj xe*w dki0zmn9ses. What happens to the distance between successive crests if the speed b p9odf0to,j ka(m. x9m 60k:ekw* jidnp59zfremains constant?

  A wave moves on a strnk6 9 s4v2oxioing with wavelength l and frequency f. A second wave on the same string has wavelength 2l and travels with the same velocity. What is the freq9ks2ivnx oo64 uency of the second wave?

  Consider a traveling wave on a string of length L, mass M, and tension T. A sty u -i*.gb iqab5/a9jeanding wave is set up. Which of theg-5b /abyq aie*9j iu. following is true?

  A string of mass m and lj;pg((y l8xz1u8vg 4l2ihnlu)n u3i mength 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 string if the mass of the string is increased to 2m, with no cuv8jnu23 1y()8m xn4ll;h igzl(uipghange in length?

  A string of mass m and length L is under tension T. The speed of a wave in tifcf .sx)1gg6 he string is v. What will be the speed of a wave in the string if the length is increased to 2L, with no change in mas6cx .i)ff1gsg s?

  A string of mass m and length L is under )clkx-6(lga.ki v hk. tension T. The speed of a wave in the string is v kxg kla kli6h)c..-(v. What will be the speed of a wave in the string if the tension is increased to 2T?

  In seismology, the S wavi 6sth )svv0qzu :kfw90fq /w3e is a transverse wave. As an S wave travels through the Earth, the relative motion between the S wave and thewsfiv3ku sq/tv6w zfh090: q) particles is

  In seismology, the P wave is a longitudinal wave. As a P wave travels ths7 j3qf6xcxlzct- ac4 .dm( l6rough the Earth, the relative motion b37.6azs cccq-(4xt m f xl6dljetween the P wave and the particles is

  The intensity of a wave il1jyq)lmj( (4p 1la itmq9v3ps

  A wave pulse traveling to the/ e8xyi 38bkgkie6 )un right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientatiy3)eg /buk8 xi8ie 6nkon of the reflected and transmitted pulses?

  Two wave pulses with equal positive amplitu,k.s8 xxx:jjyi9c or.u.;mgqdes pass each other on a string, one is traveling toward the right a.xjkcg,:.9x x s.joum;q 8 riynd the other toward the left. At the point that they occupy the same region of space at the same time

  Two wave pulses pass -fhfczu -r/p cg 9vrq28x2m6seach other on a string. The one traveling toward the right has a positive amv m2fu-9r6 f/pcxc28g- qszrhplitude, 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 the same time

  Resonance in a system, suc5+jgn p:wr g,ph as a string fixed at both ends, occurs when

  If one doubles the tension in a violin string, the fundamental frequency of 5uv y7yuk noe1 d;d)1uthat string wy7)od; y5dn1 u kv1euuill increase by a factor of

  What is the spring constant of a spring that stretches 2.a:c i/ b(8hrw2 grki3n00 cm when a mass of 0.600 kg i(hriw kg/:ncr8i23ba s suspended from it?

  A mass is attached to a spring of spring constant w0ou:k45r zs0 i,ob1kx ccyp-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 eqsbk0z:okw0o xcu,y-p 15 rci 4uilibrium position when it is oscillating. What is the amplitude?

  A mass is attached to a spring of spring constant 60 N/m along a h(difxllpua24e, x-5j orizontal, frictionless surface. The spring is in5iel pldju ( a-4xfx,2itially 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,oc((r f t+zg4q8tj)la 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 oscillatin q zttrgfo(+j(al)8 c4g. What is the frequency of oscillation?

  A mass on a spring undergoes SHM. It goes through 10 complete oscillations 1),v e 7nrjvyxin 5vyr 7x,n 1vje).0 s. What is the period?

  A mass vibrates back and forth from the free end of an ideal spring of spring co7nivgu48/4 dwe ls5c mnstant 20 N/m with an amplitude ofu g5wi8 4csl7mn4/ edv 0.30 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 sprink ,l*r 96t gyh:ww-(kuqqx gr*g constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motiouwy ,rhql-r:kqg*kw*g 6(9 xt n and has a speed of 1.5 m/s at the equilibrium position. What is the total energy of the system?

  A mass undergoes SHM with amp/rl, j bmg bz z6w;j6;v+x /tcx1yt( h*eyga0xlitude of 4 cm. The energy is 8.0 J at this time. The mass is cut in half, and the system is again set in motion withgt1 z,6y hb/ygxxwv+ez /bjm; rxjc6ta (*0;l amplitude 4.0 cm. What is the energy of the system now?

  A 0.50-kg mass is attached to a spring )mrugo 6 7q e.7ck)iagof spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple ha)7.gqr )6ckoiema u7grmonic 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 spring ofhtw cnh (spmnl5q w2) ;* h +b:stxjk)l(f6lh- 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 location are the kinetic energy and the potential energyh6k)hc bl ;n 5m-*+pq:lhw(tsxjnh flt)2s( w the same?

  A 2.0-kg mass is attached to t0o1oyix8 r.,glwzd hnq w6b0(he end of a horizontal spring of spring constant 50 N/m and set into simple harmonic motion with an amplitude of 0.10 m. What is the total mechanical energy oy 160qw b,o0x( .nr w8gdihlozf this system?

  A 2.0-kg mass is attocjmap gy4da w4 67+ig a(8a+trw,ph:ached to the end of a horizontal spring of spring constant 50 N/m and set into simplmy(ta8j4+a6gpa idg hw 4acp o+7 r,:we 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 ideal spring of sz siz evhy8b(b mmq*m-4ap496ir .j.0zs8nq bpring cob8brsb.6 4i 4z.0zym -znjqm9hqi vsp (8*ma enstant 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-spring system is dbtd+nik+5 mrlht9 s8bv6*uec0 ct-- uisplaced 10 cm from its equilibrium position aueh*istu vdkb0mrc+t8nltc- 59 -+6bnd released. 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 constang57 q6q o0g-qrk -jqtkt 10 N/m. The object is displaced bjqo7q6 kq 5r0-gk -qtgy
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 cons4l)n9-qbdhcu9pv zw 0 tant 10 N/m. The object is displaced b9 n0hq wcupvz49l -b)dy
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, dispj;pjh -fb4 aeqf: cm9-laced slightly from its equilibrium position, and released. What is the frequency of its vibrajjf49mf pc; a-:eb -qhtion?

  A mass is attached to a spring. 6 rb;jgti 2k4u It oscillates at a frequency of 1.27 Hz when displaced a distagb;6tu 4 kir2jnce of 2.0 cm from equilibrium and released. What is the maximum velocity attained by the mass?

  Two masses, A and B, are attached to different springsxa,ss:np t, w6. 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 fspwxs6,,:nt a requency 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 eqxr2wn )cmx2pd+ba m17uilibrium 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 period of osx m )17dp+ wnm2a2xbcrcillation.

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretc1d .ls.iwd23 f f/kk,cf3vjdshes 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 total energy of the system.d.cikfw3 /sj31f2ld s. fd,kv

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches the daph6,ujhgw+f3 -up *usa+ g0 spring 2.0 cm downward. The mad g+p0ufgj u3+aa6hpw, u *s-hss 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 harmonic motio,- r2a8m gof(fy9ebcln obeys the following position versus time equatl2eg89 fr ocfa,bm (y-ion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the followin .x.gtaj 98shsbgjux9w:y uk7 xfy1* ;g position versus time equation.y7yxkw1sgf;8 usb .x9 tujah x9*j: g:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the followin+0j+cpt-pkxm k1- u3qc l slg8g position versus time equgtlxjs01 q+p8-kcpm k l+- uc3ation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes simple ha,s 14,oiq ppp -tk8y xas 1etvt:u)8/7utbuyhrmonic motion according to the thu1apt )yp8is,vue s:8 17u-kxpo/b yt,tq4equation $y = 0.50 \; \sin (18\pi \times t)$ where y is in meters and t is seconds. What is the period of vibration?

A 1.5-kg mass attache,iz) :hftxijm ; matk,w2u 96ld to spring with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the mass is released :zathx f2w6,,ki ) mjl 9;itumfrom 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. ( bpvrmnayi8oavd n r.2 s/(.74a) What are its frequency and pennor y. 7 8apmv2is.bd(av4/rriod on Earth?

  A 3.00-kg pendulum is 28.84 m long. What is its period on Earth?b7v 8o+saxt r1p0q;j j

  A pendulum has a period of 2.0 s zbt4avjxj; ,g8mzx 9cb+ t4k 1on Earth. What is its length?

  The pendulum of a grandfathe(f,2t)kvjil g (b -wknr clock is 1.0 m long. What is its period on the Eagv nf2 ( kl,jw(itbk-)rth?

  The pendulum of a grandfather clock is 1.0 m long. What is ywa .1gazfn.9ob .58o2g/xj qrk,x0vxf-ht vits period on the Moon where the accelerationg.hzxkv xg2 aw.8 vfn-of95ayq1/ ob, 0tj.xr due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-kg spherical mass attached to a masn9.1i:u8tfj -h pexecsless 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 hav j9u.fc x8peiet1:hn-e 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 inieoxv xc+ 67n1w0lg.e;rttg bc.jn:a5 tial angular displacement of 8.0e. It oscillates ljxct7e v:w e.ax0trg + ;c6 5g.nbn1owith 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 time. The frequency o(s okoa. m8kxdk2/mc8 zd;ye) a7y1caf the wave is 120 Hz. What is thes od a m)k.mk788d/x(;oac 21ykceazy amplitude?

  Figure 11-2 is a "snapshot" of a wave at a given time.zp-f ut/)wjpol58rn 4 ia.zw( The frequency of the wave is 120 Hz. What is the wavelength?pl )f/5uz 8wrtia - jwop.(zn4

  Figure 11-2 is a "snapshot" of a wave at a given tim4gc ii(n8 b :co(*q4tawqi p8me. The frequency of the wave is 120 Hz. What iw t:qcci(giq4i b(np848mo a* s the wave speed?

  What is the frequency of a wave3. ao-lsbz08in pa. vw which has a period of 6.00 ms?

  What is the period of a ,i5 hpcoedh1 lq a+8b;wave with a frequency of 1500 Hz?

  What is the wave speed if a wave has a frequency of 12 Hz and a wavelength2bo;,jk*hw; ks s zal9uex :5g of 3.0 mxsaw 2;zlb *e sg,:5okj huk;9?

  What is the velocity of d-m-gaq2vyn5 a wave that has a wavelength of 3.0 m and a frequency of 1-2 5nvmday-gq 2 Hz?

  What is the frequency of a 2.5 m wave iew5, ph(q/mvhhaijhe k gt 5q 94-s75traveling at 1400 m/s?

  A piano string of linear mass density 0.0050 kg/-5lx461ogv dxerv1vqm is under a tension of 1350 N. What is the wave spe1odxq5xrvv6ge41 l-ved?

  A string of linear density 6.0 g/m is under a tension of 180 abu1vg;,ob6q mq)sr6dx2eq :e w* -geN. What is the velocity of propagatier b u6sxqq:;a6eo -v,g)bew1*mgd2qon of transverse waves along the string?

A wave whose wavelength is 0.500 m is tra+ndro n4ps) 1nveling down a 500 m long wire whose total maso sp )1nnr+n4ds 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 lo(uhd (qrj52v gng string fixed at both ends is 200 m/s. Which one of the following is not a resonant frequency of this stri h5jg(qv d2r(ung?

  If a guitar string has a fundamental fre+k0p4s ,bxz-tf,zbsv9s) k n+ecuz6 p quency of 500 Hz, which one of the following fre,t4bsz0s ,kxc +z+n6pf)- k9pubeszvquencies can set the string into resonant vibration?

  A stretched string is observed to have four equal segments in a sta xcss8gfv3c 85nding wave driven at a frequency of 480 Hz. What driving frequency will set up a stand scvcg sx8f358ing wave with five equal segments?

  A string, fixed at both en 7xcv/itbxe9 1ds, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops. What frequency is needed cx7x1 vti9eb /if the standing wave pattern is to contain 4 loops?

  A string of linear density 1.5 g/m is un* wfqblrhlh s ,4ib)82bk2g0n dut7h,der a tension of 20 N. What should its length be if its fundt4lh k)7b 8bfg20,q,2durn wlbh ihs*amental resonance frequency is 220 Hz?

  Find the first three harmonics of a string of linear mass density; 6a3vl oabz.ywb)u) l 2.00 g/m and length 0.600 m when it is subjected to t ovl;zau.ab) bw3 l6y)ension of 50.0 N.

A string of length 2.5 m is fixed at both ends. When the smt-8qeos /eu +tring vibrates at a frequency of 85 Hz, a standing wave with five luq8me e o+t-s/oops 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.