The time for one cycle of a periodic process is caltzi5*a aok:v/z 5br0pled the

  For a periodic process, the number of cycles per unit time is calledfysegide9l- j .q :h18 the

  For vibrational motion, the maximum displacement f t2fsp2x lc) *w5(iyxtrom the equilibrium point is cax(x5 ws22l*ct) t ifpylled the

  A mass on a spring undergoes SHM. When the mass is at its maximum displace l/ /w4mkl-l xlxn++bament from equilibrium, its instantaneousw/n+am lb +ll-xk/4xl velocity

  A mass on a spring undergoes SHM. Whe 1cv5g8h bo p( xs17dqgmzlu4:n the mass passes through the equilibrium positsvub1d5gp xo 8g1q mzlc(h 74:ion, its instantaneous velocity

  A mass on a spring undergoes SHM. When the msz f-++eqr*jj ass is at maximum displacement from equilibrium, its*qr+z+ -sjfej instantaneous acceleration

  A mass is attached to a vertical se)-wxxmueomp5rt x. +p0:ec/pring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a pee0u mx/p-c5m+ xw):xot .erminimum?

  A mass is attached to a ver8a96q01tx vrbsf k+s rqr nwalxp*b/a8: c7z4tical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximu9fl6w+1r:bpkvqqx trbr8a4 asc/7z8 sn * a x0m?

  A mass is attached to a vertical spring andm85x6e p(vf5qs ltckz gv(lp1 1ut*bi55p.z k bobs up and down between points A and B. Where is the mass located g1zkpl5.u*zetv5x bmpf86 c sp(il q5(5k1t v when its potential energy is a minimum?

  A mass is attached to a vertical spy:6x k)a y)0qgfzi: 0vvws8kb7z )lpc ring and bobs up and down between points A and B. Where is the mass located when its potential energy is a mspyl:0k)86) zcya xv: 0b fq gzvk)w7iaximum?

  Doubling only the amplitude of a vibrating mass-and-spring )5 rrfel na50xsystem produces what effect on the syst0xe )n a5flrr5em's mechanical energy?

  Doubling only the mass of a vibrb,7qg e 7kcle7ating mass-and-spring system produces what effect on th, q7kg7cee7lb e system's mechanical energy?

  Doubling only the spring constant of a vibl .v;9iyc uhf)rating mass-and-spring system produces what effect ;lcu)iyfh. 9v on the system's mechanical energy?

  A mass oscillates on thea.) hqn r,ib36dg r)kf*kg0cm end of a spring, both on Earth and on the Moon. Where is t0 d frg)q,ink6k3)* ambr. hcghe period the greatest?

  Increasing the spring constant k of a mass-and-spl 4cuxf, o- 2mmbqef2+ring system causes what kind of change in the resonant frequency of the sysfxqu mb4-o+c 2e2,lf mtem? (Assume no change in the system's mass m.)

  Increasing the mass M of a mass-and-spring system caus6.o uo5 xpye: 2rviz-ves what kind of change in the resonant frequency of the system? (v: 2uo .vpo6y-i5erxzAssume no change in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spring ih 6-paf-zg0st rg 9uvmzt**e 88vu9h6kjt; csystem causes what kind of change in the resonant frequency of the systh*9r zz s0uvht- -g6 89ifmt8cv*ugtj;6 paekem? (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 mskm wxgl*x 53 :ghqnh,4p:u(attached to a weightless string of length L. For this system, when undergoing small oscisq 3g* mpgk:hxhlxwm4 n5,:u(llations

  When the mass of a simple pendulum is s+,9j/tzwwz2b/e rnr tripled, the time required for one complete vi9z+ t/erz/,jwn sb2rwbration

  Both pendulum A and B are 3.0 m long. Th fc bhkd owyq92k3-/:zht.)lpe period of A is T. Pendulum A is twice as heavy as pendulum B. What/w. 3y d-fkhq k2ol9t)zcbh:p is the period of B?

  When the length of a simple pendultw 1bez:5j/fpe*v) x1.vn trtum is tripled, the time for one complete vibrat v1bz: t5tfver/tew jpx) *n.1ion increases by a factor of

  What happens to a si)40qe-nh zlicb*e an; ,q9lxby/hhu 9 mple pendulum's frequency if both its length and mass are increa9 lxh/-*elbnb0h , iq) z;a n9uyc4qehsed?

  Simple pendulum A swings back and forth at j yy9zj:48 oc:fybo-c twice the frequency of simple pendulum B. Which statement is correct?:c4jyz-j8:oyybc o9 f

  If you take a given pendulum to the Moon, where the acceleralvfea5 r ;,k4efsf b(8tion of gravity is less than on Earth, the resonant frequency of th(ksf,fflev ;rab458e e pendulum will

  Curve A in Fig. 11-1 representsa) ;, w.uszg(klyrfe 8

  Curve B in Fig. 11-1 repre1eyzb) gu8h.vfu y27z sents

  Curve C in Fig. 11-1 rrt-c vh:+fwkj h6q8 x,ziq6w g7i,,h oepresents

  For a forced vibration, thnr 1zspwvr;) f:mpl +0b bzc91e amplitude of vibration is found to depend on the

  In a wave, the maximum displacerflck131k0cw8uw t o. j3hli2 h4mu 0zment of points of the wave from equilibrium is calle 14lhfz w380ho3c lm truwuki kc.021jd the wave's

  The distance between successive crests on a wave is called the g e2yd29q dnt6wave's

  The number of crests of a wave passing a point p)psw .gp.u p0 xne+ oq//0b3 kefdn(vcer unit time is called the wave'sef+gpsnqu.w (/0/ne)dpvxp. oc 03 bk

  For a wave, the frequency d 5h 2yl91dotmtimes the wavelength is the wave's

  The frequency of a wave increases. What happe :bjjz,.6.y1y rlgv sxns to the distance between successi,yl z.6 g.vjxrj:1 ybsve crests if the speed remains constant?

  A wave moves on a string with wavelength lq ,p/x6vnro+wr ssa2(d4 tn ,z and frequency f. A second wave on the same string has wavelength 2l xv,rn/wr2nsqp (4o6+zst ,da and travels with the same velocity. What is the frequency of the second wave?

  Consider a traveling wave on a string of len,g rmc6f y b+bj.m:fl(gth L, mass M, and tension T. A standicb.lf:,f+ry(b jm6m g ng wave is set up. Which of the following is true?

  A string of mass m and length L is ,s.hxi3:wr*0wf/ w+8va.qks rkyhupa :wah -under tension T. The speed of a wave in the string is awyw0v-3wux q *8h/ rkak:sapfh:w. i r+.h, sv. 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 tension T. The speed of a wave in th;sj( x,gt+ piwk 7ss99gzblp ;e string x pj+l ws ,spk;s7gt(gb9z;9i is v. What will be the speed of a wave in the string if the length is increased to 2L, with no change in mass?

  A string of mass m and length L is under tension Tg,k dm :op+ vrz(goj:gxo8j6 :. The speed of a wave in the string is v. What will be the speed of a wave in the str: ozgg8o r,g+vj(kdx6om:j:p ing if the tension is increased to 2T?

  In seismology, the S wave is a transverse w bm qh(gsld mxs 2,91l:e+h8rlave. As an S wave travels through the Earth, the relative mh8 ml+r(2qb,1 : el9xsmsg lhdotion between the S wave and the particles is

  In seismology, the P wave is a lon/-ntyeu0 - )uu vvt4uxgitudinal wave. As a P wave travels through the Earth, the relative motion between the P wave and the partiyv-0-xtenuv 4uu)t/ ucles is

  The intensity of a wave ;+u:wu9firwo:*q ngi dl7ot)is

  A wave pulse traveling to the right along a thin cord reaches a disconti-b b 2fgnu9dx5nuity where the rope becon-gu d9 5b2bfxmes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

  Two wave pulses with equal p ke0;o 4zy3i:on 0lgn,leidv 4ositive amplitudes 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 regie04;n3kl 0oi yeg,d ozin4vl :on of space at the same time

  Two wave pulses pass each other on a strin.l es*gc zm5gk-wq03x g. The one traveling toward the right has a positive amplitude, while the one traveling toward the left has an equal amplitude in the nee * l-3wmkgzq x0sc.5ggative direction. At the point that they occupy the same region of space at the same time

  Resonance in a system, such as a string fix.n1/em jdd 679iitqn oed at both ends, occurs when

  If one doubles the tension in a violin string, the fundamental frequen iy8me q5azl. 2h4gjv0cy of that string will mv5h20e i8lzg .y4qja increase by a factor of

  What is the spring constant of a spring thatx ar+; +oua0jfd5km9si2 6zfm stretches 2.00 cm when a mass of 0.600 kg ;rff0 +aux6jm5d+z kma s9o2i is suspended from it?

  A mass is attached to a spring of spring constant 60 N/m along a horif8z,6w bpt06ff 9 tukxzontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes w b869x f0k, ft6pfzutthe 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 o kylp/ atcxowg/h25s p-*wqhy) 8b k25f spring constant 60 N/m along a horizontal, frictionless surface. The spring is initially stretched by a force o/2w-oyhwk g 2cq*lh8axy5p/) bp5t skf 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 consv,9 s.,zh) dnh1jawj utant 60 N/m along a horizontal, frictionless surface. The spring is initially stretchedwu,vjs)1.9zhad n ,h j 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 S,c, 3l;zxr h7uw nh5otHM. It goes through 10 complete oscillations in 5.r3,uc;z wn5 , h7xohlt0 s. What is the period?

  A mass vibrates back and forth from the free end of an ideal spring px hn-:odw p-5of spring constant 2h-pw -d5:xnpo0 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 its equilibrium position?

  A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizonrb;fax f*s g +m3-abi2tal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium posi arg * m-fsb3i2abf;+xtion. What is the total energy of the system?

  A mass undergoes SHM with amplitude of 4 cm. The energy is 8.0 J ay b139hpjrxd14bv 4zx84vxgt t this time. The mass is cut in half, and the system is again set in motion with amplitude 4.0 3vxd4jxb 8p114byxvt9g r4 hzcm. What is the energy of the system now?

  A 0.50-kg mass is attach xa e:0dkn)vl3 -iuu.hed to a spring of spring constant 20 N/m along a horizontal, frictionless surface. lx:-dun3vihu)k .e 0a 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 vibration?

  A 0.50-kg mass is attacyadpyj- c ,aa+efgi*dviw5 3*-3 8lpmhed to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and-w*3* layav3 dyi 5pd-+c,ajep8 gmi f has a speed of 1.5 m/s at the equilibrium position. At what location are the kinetic energy and the potential energy the same?

  A 2.0-kg mass is attached to the enu cm3*bpg-l) xd 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 mem)p -cug*3 xlbchanical energy of this system?

  A 2.0-kg mass is attached to the end of a horizontal spring of spreg2b y nhnb(,w /fx0o,ing constant 50 N/m and set into simple harmoniwfn0( eob,y,n x2b/ghc motion with an amplitude of 0.10 m. What is the total mechanical energy of this system?

  A mass vibrates back and fort92 eb,9r8gtj7qttw0def ydn ,h from the free end of an ideal spring of spring constant 20.0 N/m with an amplitude of 0.250 m. What is ,ftd,8t2d9w9 n7ber0 ye tq gjthe maximum kinetic energy of this vibrating mass?

  The mass of a mass-and-spring r.*d 7ezt mf*kf*/jibsystem is displaced 10 cm from its equilibrium position and releasedtkf .ezfm/*** brjd7 i. 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 constant 10 N/m. Thrfw m,dsm 9i 45dn g7me/area,e )-x*re object is displaced b9wd,axs f)-ermdm7e4m,i* ngr/ 5ar ey
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 , i2 q78sohzrcconstant 10 N/m. The object is displa 8hz q,sr7c2ioced 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, displafninda 9(fpbr ex +,(2ced slightly from its equilibrium position, and released. What is the frequency of its vi,9dnnxb +f rf2a(e(p ibration?

  A mass is attached to a spring. It oscillates at a freq(+x x*a6na+siwr x7+ mqk av*iuency of 1.27 Hz when displaced a distance of 2.0 cm from equilibrium and released. What qmw* v+ia rxkxx7 a +6*nsi+(ais the maximum velocity attained by the mass?

  Two masses, A and B, are attached to different springszcmx467vpnb +zr,uef1/(ym7m*tb //xudks c . Mass A vibrates with amplitude of 8.0 cm at a frequency of 10 6uu/bpv1b*c4ekxm+z(n/,md 7rysmt fzx /c7 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 the maximum speed of B?

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass v ,tl:rm8nf3iby: d+fhy8rn0stretches the spring 2.b+rhtir mf80lfy :8,ndvn3y :0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Calculate the period of oscillation.

  A 0.30-kg mass is suspended on a str l)rk(d f3j0bi.;gl p5b1dvpring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm db 3vr;kdr0 )(.1flg blpdjti 5own and released from rest. Calculate the total energy of the system.

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass streqhe bp)b y y5u6fnq6rudw0-+ ,c. qqx*tches the spring 2.0 cm downward. The mass is then pulle)yepuqc,b - b.0*q hr6w6qqxudfyn+5d an additional distance of 1.0 cm down and released from rest. Write down its equation of motion.

  An object in simple harmonic motion obeys the following position versus timecpc :.:a -j do6mqd8kw equatioqm: cwpkc 6o.a8 dd:-jn:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the following0d.e k28y.aldawnujl +p2 c0i position versus time equation:uknai0c.8 dpjaldy0+.2w2l e
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic mz v92tqcw3l5 fotion obeys the following position versus time equat3lf5w 92qvzction:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring exec zrl,wh rd-8- c:ipl6tsaz,t* utes simple harmonic motion according to the equs:td w,-rz *6pl8c a-rzt,hliation $y = 0.50 \; \sin (18\pi \times t)$ where y is in meters and t is seconds. What is the period of vibration?

A 1.5-kg mass attachelv gvu i+*l;z3j kue jcn0;dhec;*+ ;nd to spring with a force constant of 20.0 N/m oscillates on a horizontal, frictionlesldu;;0ekl v*jc*c e;; ni3zgjhnv+ +us 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 swingwx8 s q.ch81ces in 8.0 s. (a) What are its frequency and pe88 ewh.s1x qccriod on Earth?

  A 3.00-kg pendulum is 28.84 w.mll1(xdl; 5mcc/8xcc4o vp m long. What is its period on Earth?

  A pendulum has a period of 2.0 s on Earth. Whaputg 0g1 mb r,s8kd:r*.j nk2at is its length?

  The pendulum of a grandfather clock is 1.0 m long. What is ik4fytbluxl7 )d 9 -a0fts period on the Earth?4-ktxly0 7) aubdf9fl

  The pendulum of a grandtgyltmp1(fj;5 borva;09.7ut v a 7ft father clock is 1.0 m long. What is its period on the Moon where the acceleration due to gravity is onlyyr ojg ft baf1v(5t 7ap.9tmt7;lv;u0 $1.7 \; m/s^2$?

  A simple pendulum consists of z ah4f;x,b5mq/h2ge*z ez a5x 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 forth with a frequef;bxg/ 4ea*2 xmz,z hh 5zaqe5ncy 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 lfar0(3m *b .thrto-zinitial angular displacement of 8.0e. It osmztr.3*- rthf bl 0ao(cillates 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 time. The frequency of the wa k,3s cqckplsx duc4:*sa-(lx0 a, a:wve is 120 Hz. What is the amplituk :0c,4 *3q :sxa-wssx,llpdc(uaca kde?

  Figure 11-2 is a "snapshot" of a wave at a given time. The freq mbkbrr9 o/fw *,;0s)tj8wqla8nd5bl uency of the wave is 120 Hz. What is the 8rn ol0 8 /w,dbftrsk*;balq j5w9mb)wavelength?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frequency of the wavd 8*vs5;o)vk 6cjenjxe is 120 Hz. What is the wave speed?8jjsce5d*6 );novvxk

  What is the frequency of a wave which has a period of kl6/7il venj.xs;oc b7; wbl8c-ha0 h6.00 ms?

  What is the period ofpy4d+l+ tos qo4i1c 2f: 4mws/teq .my a wave with a frequency of 1500 Hz?

  What is the wave speed if a wave has a fa2jk u1 m98fwxk wfi +ws42s,mrequency of 12 Hz and a wavelength of 3.smki9k sj4f2f 1w ww2,a+x8 um0 m?

  What is the velocity of a wave that has a wavelength of 3.0 m and a frequenc8 x+rhcsq9io 3gnfln88puw- ) y of 12 Hqu-n8fw rx38s i9g+cho )lpn8z?

  What is the frequency of a 2.5 m wave)vwkz1 ;bl8 lu traveling at 1400 m/s?

  A piano string of linear mass density 0.0050 kg/m is under a tension of 13(7)y9kmnm o +ziea;rv50 N. What is the wvr 7n +m()zy;aikeo9 mave speed?

  A string of linear density 6.0 g/m is x8be5wjiqec .0p4dm69 2z mxgunder a tension of 180 N. What is the velocity of propagation of transverse waves alo i.80wmx 2p56megx4jbe qzc9dng the string?

A wave whose wavelength is 0.500 m is traveling down a 500 mm643 dp7 i.x ne*n(+uzwsc72frbyyd u long wire whose total mass2swd zc6mp(xr y+b.*3nf4iue 7nd7uy 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 propan; h( 2szdgjda,0dr4zgation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s. Which one of the following is not a s;( j dndh24dgz0rz,aresonant frequency of this string?

  If a guitar string has a fundamental frequency of 500 Hz, which one of t/o2fjz 4 0qlnomnoe82 he following frequencies can set the string into resonant vibrati22nq4om/o j0nzfe8l oon?

  A stretched string is observed to have four equal segments in a standing 8h57i3 ncuql sp)4 ;lli6bvshwave driven at a frequency of 480 Hz. W n7 ;l4lh5)sipuhbsc li8 36vqhat driving frequency will set up a standing wave with five equal segments?

  A string, fixed at both ends, vibrates at a frequency of 12 Hz with a standing rjoh 77h0 :zf)drdo; ztransverse wave pattern containing 3 loops. What frequency is needed if the standing wave par r7fj7; dzho):z0 ohdttern is to contain 4 loops?

  A string of linear density 1.5 g/m is under a tensioyb833i)e gas bua, q9qn of 20 N. What should its length be if its fundamentqaab ,ebu3qg9y i3 s8)al resonance frequency is 220 Hz?

  Find the first three harmonics of a strintqqo ibe7p591csh d0( g of linear mass density 2.00 g/m and length 0.600 m when it is subjected to teht0esc 1 7 p(o5iq9qbdnsion of 50.0 N.

A string of length 2.5 m is fixed at both ends. When the string vibrates at a g:(-5wt ciofc3 hzy s+freqw+y-3oi(fsczcht g:5 uency of 85 Hz, a standing 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.