The time for one cycle of a periodic process is calledeczni m+*p q9j;ew,b+ the

  For a periodic process, the number of cycles per unit time is called tbioyz 2e 65+gdhe

  For vibrational motion, the maximum displacement from the equilibrium poinv-(m 9 tdqoqw) cl, f8,sqyu,gt is called themylo 9-,8vg,q(ucqsd twf, q)

  A mass on a spring undergoes SHM. When the mass icws kg1wpd; 50* 92oy+ e7e8jlbfzsybs at its maximum displacement fro 1s*sebj8f5bg0c p 29d 7;zokwwly+y em equilibrium, its instantaneous velocity

  A mass on a spring undergoes SHM. When the mass d3- h w( qomvxrr. qw8-i*1uu+sy lb1xpasses through the equilibrium posix (+mvqb3 uwx o d1q1 h.rl--*rys8iuwtion, its instantaneous velocity

  A mass on a spring undergoes SHM. When the mass is at maximum displhco 4lzl00p0w;+8 urmzkf b s+acement from equilibrh ro0l+l+c8bz 0k mw4szf0u;p ium, its instantaneous acceleration

  A mass is attached to a vertical spring a *pom y ehm97rmal(3y/nd bobs up and down between points A and B. Where is the mass located when its kinetic ene e (m39 yolhr*7pmm/yargy is a minimum?

  A mass is attached to a vertical spring and bobs up andw59 z*+tq0qukdwz k.j5k1 d xtm u0f+b down between points A and B. Where is thew z0dd0*m uku+5wtfkbqt. kz q591xj + mass located when its kinetic energy is a maximum?

  A mass is attached to a vertical spring and bobs up and down betweene:rvv fd xj*vg .1pq59 points A and B. Where is the mass located when its potential energy is a*v9 p5xj:dfvgv .rq e1 minimum?

  A mass is attached to a vertical spring and bobs up 4e0cvgcp99 x tand down between points A and B. Where is 4pc eg099vt xcthe mass located when its potential energy is a maximum?

  Doubling only the amplitude of a vibrating mass-and-spring sy; /p(1/ hhdkwgcj8 41 ayd:xvgg37pk 9sc dtjastem produces what effect on the system's mechvh /pt1a9(s1;kcyad 4:cgj/j3gdd7g xwkhp 8anical energy?

  Doubling only the mass of a vibrating mass-and-spring system produces whatifnzp- ni. o9ok4vt;ui 0kymvz8(b*- effect on the 90o o fin mi.;-vu*8vzz-4y (tk knipbsystem's mechanical energy?

  Doubling only the spring constant of a vibrating mass-and-spring system pr l ;3tbdwp2b:poduces pt2 l3b;wp :bdwhat effect on the system's mechanical energy?

  A mass oscillates on the end of a spring, boxd q+q+0z89vsvm 4wgm1 l1p ugqya(j5th on Earth and on the Moon. Where is the p9swdm xu5m1l v41ga y(jgq0vzp++ q8q eriod the greatest?

  Increasing the spring constant k of a mass-and-spring system causes f6o(,2r,c)qvmiq yjiwhat kind of change in the resonanyviq (r)c im,fq6,2jot frequency 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 changedt1kbmx s48wfj+ft2 ub;pn1o3n ( ) ly in the resonant frequtsjn 21xdkny 1up8fw( bmt+ 43f)o ;blency of the system? (Assume no change in the system's spring constant k.)

  Increasing the amplitude ow f1ft,6u8qo;gx))nk, i(shn6g dnosf a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Asgd6w),8gotfnhi(x)1fosks6 q ;u,n nsume 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 to a weightless string 6 *xilzj1yt,rpr1x0q fpo((sof length L. For this system, when undergoing small o,ixrqy(s01xpopf j*(6r z1 tlscillations

  When the mass of a simcx.0cs r *qz0uj4,do uple pendulum is tripled, the time required for one complete vibr,o x *uj.0 4c0zsrqcudation

  Both pendulum A and B are 3.0 m long. The period of A is T. Pendulum A7 u2 kf5x8yo ycwdm9f( is twice as heavy as pendulum B. What is the pero 8y dwuyx5cf9fkm72(iod of B?

  When the length of a simple pendulum is tripled, the time for one complete au ue- fdj0yz:.u+v,q y3 x:vcvxmc*:vibrauauuvey0m j.cxcd, f:xz-qy +:v v:3 *tion increases by a factor of

  What happens to a simple pendulum's frequency if bot b4 : m96+e5dpgsnfc*y5svaivh its length and mass are increased ape4 5nb96:v+5mciv sdf*gys?

  Simple pendulum A swings back and forx/nhl hh,:2 qath at twice the frequency of simple pendulu/: n2,q laxhhhm B. Which statement is correct?

  If you take a given pendulum to the Moon, where the acceleration of gravity is ld 3tl* otd43pei2b gn4gh2v 1 nj*w0aqeg 4igtw qo dn h2123abl* t0d4v3n*pjess than on Earth, the resonant frequency of the pendulum will

  Curve A in Fig. 11-1 represenadfl; b6 ,ffuq3 el4 5t1perb;ts

  Curve B in Fig. 11-1 repreg55f wdsx c ,fp85xc,fsents

  Curve C in Fig. 11-1 repreor g:.,5z*mt l:rij posents

  For a forced vibration, the amplitude of vibratiiy m4+up/ 1o vas-2tdwbn,-xcon is found to depend on the

  In a wave, the maximum displacement of points of the wave from equilibriumhe/;,v 1b6ooj( zpj cr is ca, ;o(czv/6ojbhp jr1elled the wave's

  The distance between successive crests on a wave is calllx k/ykq-kt ba.-09rped the wave's

  The number of crests of a wave pas 5(ak lyxqf+*dsing a point per unit time is called the wave'y(la*5+xkf d qs

  For a wave, the frequency times the waveleng g u0un,2ouivlcc l wf4;l-h-;th is the wave's

  The frequency of a wave increases. What happens to the distance between succetmsauo3 8q gj( /pkl);xd9xet*: hnj5ssive crests if the speed remains c; gde*j9 x)5xhl/3paqok8 j( tmsun: tonstant?

  A wave moves on a string with wavelength l and frequency f. A second wave ftef 5l. el1l*on the same string has wavelength 2l and travels with the sam1ffte ll*.e 5le velocity. What is the frequency of the second wave?

  Consider a traveling wave on a string of length L, mass M, and tension T. l8z - o 3v-u g-th5z(hu nu*hz/qyysq3 A standing wave isnqu u-o(hhtsl5--zvzgu/q h8y3y *3z set up. Which of the following is true?

  A string of mass m and length Lboo)5h 3 o q)m4vox7xoepx m )qln3,.j 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, wipo,e4xl)jxm))3o5h 7.b mooo xq nq v3th no change in length?

  A string of mass m and length L is under tension T. The speed of a wave in tn-l)fn. hr/rq he string is v. What will be the speed of a nr. /qhlrf-) nwave 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 T. The naiypr6;g h jl:4g qgu h663(yspeed of a wave in the string is 63 n4jhly(r6yai6ghu ; gg :pqv. 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 wave. As an S wave travels t6wj s(koxb+:kn hoc a.6woh97 ms5a0phrough the Earth, the relative motion between tops 6boa w7sk an6 5+0.j(hwoh:mckx9he S wave and the particles is

  In seismology, the P wave is a longitudinal wave.c *i- tt2o/5u.pdqyj a As a P wave travels through the Earth, the relative motion-*/2t5 uqci opy .tjad between the P wave and the particles is

  The intensity of a wave isk6:7 ilf9wjbp

  A wave pulse traveling to the right ailc-)7ij3ap0e 5hy m along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the pi elci5 ym307aah j)-orientation of the reflected and transmitted pulses?

  Two wave pulses with equal positive amplitudes pass each other on a strirufo/ g cui;lw277bvs f7x(m;ng, one is traveling toward the right and the other toward the left. At the point that they occupgb72 ifvxuc;rm; 7u(fw /lo 7sy the same region of space at the same time

  Two wave pulses pass each other on a string. The one traveling towarvt ql;,(ai+ t dj.ou7bd the right has a positive amplitude, while the one traveling toward th+7uo ;l.a b(dtt ijv,qe 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, such as a stri2mg vq-v )ixo5:e2vtgng fixed at both ends, occurs when

  If one doubles the tension in a violin string, the fundamentkhg0vyb,t wmsw. l4srx9,/k 6av):jkal frequency of that s/w,0ak.jwhrb4t kgm9 )6 lv,vysk:x string will increase by a factor of

  What is the spring constant of a spring that stretchesar b hls* ps(m02xn+y4 2.00 cm when a mass of 0.600 kg is suspended from itsbx0l*nsrh4 py(m2 + a?

  A mass is attached to a spring of spring constant 60 N/m along a horf2vor cxs7)e2qy/f hu7 ms +v(izontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes t+e7cxhfyf v)qv/s r722um o(s he 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 along a horizont cn4t(urx7 z-pal, frictionless surface. The s p7-zxnc(utr 4pring 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 horizu,a2e90bkd n iontal, 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 db2k09i u,enais oscillating. What is the frequency of oscillation?

  A mass on a spring undergoes SHM. It goes through 10 complete oscillateu m 1a09ukunv)d ei3qdd -a85ions in 5.0 s. What is the)e 01avqa8ndu iu- me dd9u3k5 period?

  A mass vibrates back and forth from the free end of an 00w44tqa ezegideal spring of spring constant 20 N/m with an amplitude of 0.30 m. What e0t4 we04zqagis the kinetic energy of this vibrating mass when it is 0.30 m from its equilibrium position?

  A 0.50-kg mass is attachleb0ii 4a,98 mbs/djs q4k2jled 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 q ijs 48m/b2 4s90ldaijlkeb,equilibrium position. What is the total energy of the system?

  A mass undergoes SHM with amplitude of 4 cm. The e yh-fxu 6 7a3-f0flacenergy is 8.0 J at this time. The mass is cut in half, and the system is again set in motion with amplitude 4.0 cm. What ifaae7-u60ffh-lx c y3s the energy of the system now?

  A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a hod(zqw kv(2un/j x1 b+puvypd 8k)5j2a rizontal, fr/zk)p(jap j(u8ud51dvn w2xy+2b vkq ictionless 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 vibration?

  A 0.50-kg mass is attached to a spring of spring constant 20 N/m az ac p.99oezj25j0 kqalong 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 energy tcjz5099aj q2p zoake .he same?

  A 2.0-kg mass is attache;(ky owl,v3u3 d+d )kfajj3rad to the 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 d,3k3 ) wul3jv(djra +a;kfyo mechanical energy of this system?

  A 2.0-kg mass is attached to the end of a horizontal springh7esqtvds*e;j cwis 6-b3o 4( of spring constant 50 N/m and set into simple harmonic motion with an amplitude of 074 hvs-3 e*cj sb;ioedq6(ws t.10 m. What is the total mechanical energy of this system?

  A mass vibrates back and forth from the free end of an ideal 9x dbnj8ksl3ccl 47 .bspring of spring constant 20.0 N/m with an amplitucnld7kbx j 94 .bc8ls3de 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 equn20 7nojnruy *ilibrium position and released. A frequency of 4.0 Hz is observed. What frequency would be observed if the mass had been displaced onl ynr2nounj *70y 5.0 cm and then released?

  A 4.0-kg object is attached to a spring of spr cf* bw4wnkq 1/3o5lwhudk(+ting constant 10 N/m. The object ikl4 kqw(3 5b +h/nufcdoww*t1 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 sprn iot kv(r j)i: s7lk:8ia hbkjg13+0,,dze tming constant 10 N/m. The object is displaced:sl,tbv r(g1:i8t,hj)ki izk7do3 nj e+mak0 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 constkm1 g2 awln75tm qz;h+)gfz;m ant 18 N/m, displaced slightly from its equilibrium position, and released. What is the frequency of its gq kml 7;fmz2a+z1tgw5 ;m hn)vibration?

  A mass is attached to a uad 5r7rhr 92yspring. It oscillates at a frequency of 1.27 Hz when displaced a distance of 2.0 cm from equilibrium and released. What is the mr dry972uahr5 aximum velocity attained by the mass?

  Two masses, A and B, are attached to diff g wah*10s tk0w/gugj8erent 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 speg* 8tagw/1k 0gh0w sjued of A compare to the maximum speed of B?

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches - imf*1deng,n5c s3ptthe spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 1 m cnfg-tiedp *n3s5,cm down and released from rest. Calculate the period of oscillation.

  A 0.30-kg mass is suspended on a sprinanfs /s-6 l+0u. haorc /(o-qbt m1qlrg. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional dist m/aulstrrsq-(+ /h0c -fo 1l n6qoba.ance 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 equilibrium the mass stretches to: -c) qrk5wtxhe spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Write down it:kto q)wrxc5 -s equation of motion.

  An object in simple harmonic motion obeys the f+ emu5htkl7sy ,5. ,)gqrysfxollowing position versus time equatione5uxrkm, q5g+7tsy sy lf).h, :
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the follow9l1i)eqi 2: 1 dfnpyhaing position versus time equalqf:p9 ) ain1 ydi2he1tion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following position versus time eboe6c b.7 j:cr tnyz7+quatiy r6b.n7jctzc+ o7:b eon:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes simple harmonic motionvyg. 2r wbh.iz 1f9ys3t76nbx accordig6t1 fs .y7by9h2w.nr v z3xibng 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 sprihw..ox5*pth3t qo2 fqdm q ;x*ng with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the massq.oq2p3hmf5t*xx twh *. doq; 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 swiymt:b-g. +9j6v5gf+fo wfqg kngs in 8.0 s. (a) What are its frequency and period on:9f.q to+bg-g vgm6fj5 yf w+k Earth?

  A 3.00-kg pendulum is 28.84 m long. What is its peri/ wywqe 96wy1fod on Earth?

  A pendulum has a period of 2.0 s on Er8cs7 /te)vy ,1axjrs4 vym ;o sol)5rarth. What is its length?

  The pendulum of a grandfather clock is 1.0 m long. What is its period on the Eacc m,yh(0 seefymb6t0/ p-h3wrey 0/be3-ht,cf( p 0w6smmchy th?

  The pendulum of a grandfather clock is 1.0 m long. What is its peri-hfkeu2cpb.( od on the Moon where the acceleration ukh f-ce bp(2.due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-kg spherical mass attached ;flxqbn5:; kufbsr .,m) o:gwto a massless string. When the mass is displaced slightly from its equilibrium position and released, the pendulum swings back and forth wil::),km n rbuq5w.bsgf;x;f o th 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 angular disp i7ncff5xf)mv6( qj2;y9j y hblacement of 8.0e. It oscillates with a peri yf)(jqv9bh;y7 f652c xin jmfod 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" ov(5yk uerm8l/ f a wave at a given time. The frequency of the wave is 120 Hz. What is tuky5rlv m(/e8 he amplitude?

  Figure 11-2 is a "snapshot" of bkw b:h.hw7oc5h k2) va wave at a given time. The frequency of the wave is 120 hwvk.hh co2)bwbk: 75Hz. What is the wavelength?

  Figure 11-2 is a "snapshot" of a wave at a given time. dh;:p ,30 ni 7vrc3mbmza vp+p The frequency of the wave is 120 Hz. W :,b3dr 3pia0v;7 vppzm chm+nhat is the wave speed?

  What is the frequency of a wave which has 1r) rhlk;q6s l ;p8jjea period of 6.00 ms?

  What is the period of a wave with a frequency of 15o/(a4j 2 9sv+r abita26bzoj k :o7nra00 Hz?

  What is the wave speed if a wave has a frequency of 12 Hz and a wavele 6s9(tqvd mf73qoinu4f v2ox.ngth of 3.fsudnq f3iv v t4q(o. 2m6x7o90 m?

  What is the velocity of a wave that has aj) y/:ox*gqmuy+u 7) av4 wntq wavelength of 3.0 m and a frequency of 12 )q qmajy4yw+ u):7*t/xvon g uHz?

  What is the frequency of a 2.5 m wave travel 7x -xw+nu(emy mt05uhing at 1400 m/s?

  A piano string of linear mas6 fxj- gmit6,y: cw+t0ldy j(ds density 0.0050 kg/m is under a tension of 1350 N. What is th cfxlg: ,dw(yiyd6jtt+ 6-0mje wave speed?

  A string of linear density 6.0 g/m is under a tension of 180 u.ec6 zy/pp;i-2crj3l*mww y 4 jm)ze N. What is the velocity of propagation of transverse waveyp *zmji)cm3 ;uz/ 4wl2rewc6-py .ejs along the string?

A wave whose wavelength is 0.500 m is traveling down a :2w 0cqdb2hk o 6.h9 quu,yjdl500 m long wire whose total mass i.ul dqwyq:do j0hb,6 uc2h9k2 s
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 ha j3v(q0ibrj h2 *8gf2.0-m long string fixed at both ends is 200 m/s.2ifh3 jab*gqr(hv 8j0 Which one of the following is not a resonant frequency of this string?

  If a guitar string has a fundamental frkgaf*hfl))4+ z wyjd( equency of 500 Hz, which one of the following frequencies can y)k*(f+flhjz )wga4 dset the string into resonant vibration?

  A stretched string is observed to have four equal segments in a s5v q khh:eqp- d61a6fj,1mxlvtanding wave driven at a frequp,6xhfj1ah6vk:e q- vmq dl15ency of 480 Hz. What 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 sta1:pk1z-e :hadttpki 3nding transverse wave pattern containing 3ihpdkzte: ptk1a1 :-3 loops. What frequency 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 oui/acdo (u6o in,mo, oaqc)+1f 20 N. What should its le ca1/6(o+nqaioo c, iud m,uo)ngth be if its fundamental resonance frequency is 220 Hz?

  Find the first three harmonics of a string of linear mass density5*s13zfquom g bc3 hy3 2.00 g/m and length 0.600 m when it sc3*m o3 5yzf3gq h1ubis subjected to tension of 50.0 N.

A string of length 2.5 m is fixed at both ends. When the string vibrates apz ;s6q07*enbnvno-t t a frequency of 85 Hz, a standingzn 7ne*vqpn6t 0b- o;s 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.