The time for one cycle of a periodic process is called /t(km :mmk.i( ouo8f a9a1gia the

  For a periodic process, the number of cycles per unit time is call;qrm )9/6cmm f u(fsrked the

  For vibrational motie*:if x0to8f sm g/i2eon, the maximum displacement from the equilibrium point is called t/e*0msi x 82:fte iogfhe

  A mass on a spring undergoes SHM. When the mass is at its 4uq 7(w+hxd ceio ,;/ 7nvxmndmaximum displacement from equilibrium, its in7n(4xweinq; dmc o, xh/dv+7ustantaneous velocity

  A mass on a spring undergoes Sj;u;fjeii d/y8s ezyg4zbjz/70i;g 90xld)mHM. When the mass passes through the equilibrium position, its instanexj )u j; 8g/0m/4;ij bgz7szefdl y;iyi09zdtaneous velocity

  A mass on a spring undergoes SHM. When the mass is at maximzp.lq a5pu.wl,, h4ne* svov*um displacement from equilibriumq *szwv5.e.4phl,u*anlp o, v, its instantaneous acceleration

  A mass is attached to a vertical spring and bobs ut k(u u)us) qzd8gail 08i+fj.p and down between points A and B. Where is the mass located when its kinetic energy is a u uf8auqdkil8t .s(jz) +i0) gminimum?

  A mass is attached tog 4pk5uf*6;gj s qyzt5 a vertical spring and bobs up and down between points A and B. Where is the mass locat pt5;f* 5zyqksg4g u6jed when its kinetic energy is a maximum?

  A mass is attached to a vertical spring and bobs up and down betx(o0vh;;p-yykm mcm- mj9sg ;ween points A and B. mycxym9 g hom0;;mps(-;-jvk Where is the mass located when its potential energy is a minimum?

  A mass is attached to a vertical spring and bobs up and down betwek7ty 3m hbay,k c(w(h9en points A and B. Where is ahh k(, by9mky7(w c3tthe mass located when its potential energy is a maximum?

  Doubling only the amp4fg7nm b2xg+ fcgt2 q.litude of a vibrating mass-and-spring system produces what effect on the sysgt2x 4gf.m+2nqcg b7 ftem's mechanical energy?

  Doubling only the mass of a vibratic63 6w vaev) xylps,,dng mass-and-spring system produces what effect ospcl 3d yv,)6a e,6vxwn the system's mechanical energy?

  Doubling only the spring constant of a vibrating mass-and-spring ;bwtbk8, rfd l72r1r jsystem produces what ebr8rk;7dtwjl f b1r,2ffect on the system's mechanical energy?

  A mass oscillates on the end of a spri h cz odvy-.z3cn2eu85ng, both on Earth and on the Moon. Where is the period the greac5vuz38 ec zy-.2h nodtest?

  Increasing the spring constant k oztqnkkz5 - ccma7*l5 :f a mass-and-spring system causes what kind of change in the resonant freque-5*7cqz :zcml knatk5ncy of the system? (Assume no change in the system's mass m.)

  Increasing the mass M of a mass-and-spring system causes what kind8mi w+qpltc0. ol sa5:l2hzp1l q0*ak of change in the resonant frequency of the system? *slia q:58+qzt0 2pakl .pm 0clol1hw(Assume no change in the system's spring constant k.)

  Increasing the amplitu tq j31kd+2 oxg97mpvxde of a mass-and-spring system causes what kind of change in the resonant frequency of the symtgpx+k19 3q7d 2jvo xstem? (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 at-kp s3d,yw::z so6:ado9pk8-zd m igbtached to a weightless string of length L. For this system, when undergoing small oscillatiodi o 8:6y 3s,bz -ks:z-wga:9pdpokmdns

  When the mass of a simple pendulum is tripled, the time required for one comple49smauq;x *a0omo w ;tte vibra04w*um toa9 a;xs q;motion

  Both pendulum A and B are 3.0 m long. The period of A is T. Pekx w(ksap7eoo;8 u) +rndulum A is twice as heavy as pewe8x ;+rk)spo(7 kouandulum B. What is the period of B?

  When the length of a simple t fa(n nbe4mn i a tobmh6d/8wz6.:8;i*toq*kpendulum is tripled, the time for one complete vibration increases by a factot*tn6wnb :46*8adbm ;e8tqfim .a oi( /ozhnk r of

  What happens to a simple pendulum's frequency if both its len5l o-q) r /s;rwfp)ersgth and mass are increased?s s-;lw/efpq )5r)o rr

  Simple pendulum A swings bacb24zzy 9uby+ ke 20fvbk and forth at twice the frequency of simple pendulum B. Which statement is correct?f2y z +bb4ev90u2y bkz

  If you take a given pendulum to the Moon, where the acce(2layoy w92aao 74zsl7lac zi(m*0sj leration of gravity is less than on Earth, the resonant frequena0*z27 al4yyo2cj(s la(a9z7wi s olmcy of the pendulum will

  Curve A in Fig. 11-1 r iunuf- zxnk- z,bd8/9:rxi2xepresents

  Curve B in Fig. 11-1 represend(*j h.h;rf ommzy; jl0v xs1)ts

  Curve C in Fig. 11-1 represenm :+66 l);s1(edoegxt iaqdlbjek 6g 3ts

  For a forced vibration, the amplitude of vibration bswqwrj1on5 oa, (xx 2 29gtb(is found to depend on the

  In a wave, the maximum displacement of points of (a+sp2 q+lzwvthe wave from equilibrium is called the wa+ asz2v+( wqlpve's

  The distance between successive crests on a waoszng xy4 l8ig u(d y5*u4x+vh9fi9y /ve is called the wave's

  The number of crests of a wave passing a point per unit time is called the m2; f798jrp rvs1 onjeokqe 27wave'sjr9pje7 oe2k;8fomn1vrs 72q

  For a wave, the frequency times the wavelength is the wav+ qh/q(edzu a)e's

  The frequency of a wave increases. What happens to the qu v, z6r4yerlo+az hz:823lpdistance between successive crests iv63yl qra8hzz: eu+ 4 ,p2orlzf the speed remains constant?

  A wave moves on a string with wavelength l and frequency f. A secondhy,rz7s (;x4(nwv 3 haok7 1bmpqm+bj wave on the same string has wavelzmyh(a 4 h;x7 3 bqj7,wo1+bpnrs vk(mength 2l and travels with the same velocity. What is the frequency of the second wave?

  Consider a traveling wave on a string 8 wug jg7t5xy8of length L, mass M, and tension T. A standing wave is set up. Which of the ugj8g7xt y85 wfollowing is true?

  A string of mass m and length L is under tension T. The speed of a wave in the 7g0ry nqnyo .+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 change in leny+yn0. o qrg7ngth?

  A string of mass m and length L is under tension T. Th.doy08e2;k0wzmx i haizy 6t,e speed of a wave in the string is v. What will be the speed of a wave in the string if 0e,zw az6t08mky2x oid ;hy.ithe length is increased to 2L, with no change in mass?

  A string of mass m and length L is unig iv:gkxeu9)/nwq .6der 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 tension is increased to 2T?)nu.w9igqk6 :i xve/g

  In seismology, the S wave i:.6nx,oqlag+n zhjz t9rx*c,s a transverse wave. As an S wave travels through the Earth, the relative motion between the S :zro,jzna,*.6q g 9t hxl+nxc wave and the particles is

  In seismology, the P wave+eh f:snuo+/fm 2+a ie is a longitudinal wave. As a P wave travels through the Earth, the relative motion2num:s+f / eeoa++fih between the P wave and the particles is

  The intensity of a wl*ddd5 i:pnu+s -r7 jiave is

  A wave pulse traveling to the rixo,.khp q.k4rpbi:pi dx; w47ght along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflec:.p4 , ;kkx hwr.idppo4bxqi7 ted and transmitted pulses?

  Two wave pulses with equal positive amplitudes pass ew2 r(qof2oips + g*/eqw./rdeach other on a string, one is traveling toward the right and the other toward the left. At the point that they occupy the same rowoq/ r.s*fwed+pq(i rg/2e2 egion of space at the same time

  Two wave pulses pass each other on a strindur5y dvn g2wu34y. /ug. The one traveling toward the right 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 same region of.d 4dunu25 gvwry u3y/ space at the same time

  Resonance in a system, such as a string fixed at yt.a)9 qn8x vaboth ends, occurs when

  If one doubles the tension in a violin string, the fundamental frkba7n-f52+7-bdq 9l)y q wvi meou 1knequency of that string will increase byaflk o2 9 7-em7ybq+qn 1k)u vnibw5-d a factor of

  What is the spring constant of a ic5 ;)jrupea,spring that stretches 2.00 cm when a mass of 0.600 kg i,a)5iecpju ; rs suspended from it?

  A mass is attached to a spring of spring constant 60 N/m along ,; 31l ot 4kuwxsiayjr2f f3*ta horizontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and let go. It takes thel;ya4ts* rot 2k3jfif1,3w ux 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 cons 632emmezpfp7tant 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 oscillating. Whezme2fm37 6ppat is the period of oscillation?

  A mass is attached to a spring of spring constant 60 N/m along a horizd myvg 1y;*:nvuw::csontal, frictionless surface. The spring is initially stretched by a force d1;us y:nvm: cg:wy*vof 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 SHM. It goes through 10 complete os2jr hne,op7 i/cillations in 5.0 s. What is the perrhji7,2no e p/iod?

  A mass vibrates back and forth from the free end of zv hair9c +s 04fp(l0pan ideal spring of spring constant 20 N/m with p 9s rih4f+zca0(lvp0an 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 e2d p6gpc),+ lcc *wuzsic-8*zk2wvba horizontal, frictionless surface. The object oscillates in simple c2w26l *d*pew )zub8ks-vcc cz,g +piharmonic motion 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 amplituwv;0 i5f: -, z by3iofk/nxoadde 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 motio/od o a:nb5k yx3ii-0vz,ffw;n 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 alongfldkmp9y4b u4k-t :: g a horizontal, frictionless surface. The object oscillatgkb4ytm:4 l pf:kd-u 9es 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 mcjj)6ewygx*lt8r 5 8spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a s)cg r*jy8 tj6mwelx 85peed 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 tf0yxv 29;2xxdln l9ybo 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 totab9x;2yn xlxy29vl 0dfl mechanical energy of this system?

  A 2.0-kg mass is attached to the end of a horizontal spring gtf4 s4 mz*kk p2-3btjof spring constant 50 N/m and set into simple hzb g-4ksk342*t fpjmtarmonic 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 spr)n e5hzp8v qr tti48yt/v 2nq9ing of spring constant 20.0 N/m e/)2vrq4t9 z8 t h yinpvq5n8twith 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 equilibrium pov8v5 z0 ; pk1ykwlvp14;okilqsition and released. A frequency of 4.0 Hz is observed. What frequency wk wpl15k;v;l81qvz0kyi p ov4ould 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 constantqr 8h .6gtumd4.zoaq5 10 N/m. The object is diaum5d h tq64r8oz..qgsplaced 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 N/m. Tyelse5 s,qp 5(na;qh+tb u 7o1he object is displauy 1a;5 oq5b+7ptsle sn(h,eq ced 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 sprfnh.za8ij;5j2c +tz dmbm+ ;ming constant 18 N/m, displaced slightly from its equilibrium position, and released. What is the frequ;zmmt;d285 am+zc fnhj+ ji.b ency of its vibration?

  A mass is attached to a spring. It oscillates at a8d(op* n62 6ri zw:on(h puxyt frequency of 1.27 Hz when displaced a distance of 2.0 cm from equilibrium and released. What is the maximum velocity attained by tn:pow i6 norp8d6zy2tx *uh(( he mass?

  Two masses, A and B, are;cozor :z)e .m attached to different 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 .ro)m:e z ocz;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 stretch8jt-d bg bk0c,es the spring 2.0 cm downward. The mass is then pulled an additional distan0jbb,ktd c-8g ce of 1.0 cm down and released from rest. Calculate the period of oscillation.

  A 0.30-kg mass is suspende3x -3zambr*au+ fdy6pzrp7o *d on a spring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional pyuo*r x*f36- 7a d+zrbp3azm 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 spring.7z5s,vp ;ngrr 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 frprg5;nv z7sr,om rest. Write down its equation of motion.

  An object in simple harmonic motro+te d7o-iytg2(tzz.it6-g ion obeys the following position versus time equatt+z67tid. etrgy (ot- z g2-ioion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the following position versus time sqi d. puen,m8wc8e1fetz 5:3equ. z:8dn5i,efp8qm wu s1ec3 etation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following positiot qi.)en h+zm6n versus time equatiom+tz)6 .nhqi en:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end ap hh nd+6s0*y -jezy jffda g 8+xp*-pmc2q9,of a spring executes simple harmonic motion accorq9e 6fp- y0ahafspmz -c2xjp+ndgj* + *,h8ydding 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 force constant of 20.0 N/m o .f32h8al cozvscillates on a horizontal, frictionless tracl.ch fz3ova 82k. 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. b y;b l5,omfx7(a) What are its frequency and period oblyb;x mo 7,5fn Earth?

  A 3.00-kg pendulum is 28.84 m long. What is its period on Earlwf22i6kc;6s1yvme-yt j s1yth?

  A pendulum has a period of 2.0 s wevn:/q 9m9shp 08pv hnlt,c,on Earth. What is its length?

  The pendulum of a grandfather clock ,) ib3ta zrkb xj7gv;:is 1.0 m long. What is its period on the Eart3girb,t:avb k7zxj;) h?

  The pendulum of a granxz,7( (3yulove bv*k wdfather clock is 1.0 m long. What is its period on the Moon where the acceleyv (ke(7, l3zouxvwb* ration due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-kg spherical mass attached to a massless3ja.vu hkih9j)p i.3 az/ sq1u 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 attached to th/ihukahp9qv 3) j az.s.u1ij3e string instead?

A simple pendulum consisting of a 20fr:a 7cvre rue ;08nbck.4 3en-g mass has initial angular displacement of 8.0e. It oscillates w03bv4 eec.7 rk: re n8nu;acfrith 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. ;*d-bs--bafzy zeq/ q The frequency of the wave is 120 Hz. What is thz a--byqeq d*bsz -/;fe amplitude?

  Figure 11-2 is a "snapsho; th;tog:,tv i3p. inp3:yplv t" of a wave at a given time. The frequency of the wave is 120 H l tp ,pgv i;::.;typ3tonh3ivz. What is the wavelength?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frkmq yq:h2e * )9s;htgg*aprs 4equency of the wave is 120 Hz. What is the wave *taq)2;s q:h*ye9 k p4shgmgrspeed?

  What is the frequency of a wave which has a;y 4a clr.ml(g period of 6.00 ms?

  What is the period of a wave with a frequeafb ,:z,oqcf;x:e2 cmncy of 1500 Hz?

  What is the wave speed if a wave has a frequency of 12 H4l:; 37upufk+3 s( ncfpjoucz z and a wavelength of 3.0 m?uj lnosfcp(;p + u4f33kcu:z7

  What is the velocity of a wave that b hpj gg2w8 *6j(hooa 2mq4+xyhas a wavelength of 3.0 m and a frequency of2*jj(oggx2 qby+opa w8 4h 6mh 12 Hz?

  What is the frequency of a cc1n(m:xd:l wc8mjg; 2.5 m wave traveling at 1400 m/s?

  A piano string of linear mass density 0.0050 k1 nz 3bwu(wvw,g/m is under a tension of 1350 N. What is the wave spewbwu( 1nz3,v wed?

  A string of linear density 6.0 g/m is under a tension of 180 N. What is t q33mi+glw)leg; pyb4he velocity of propaga 4iglpmlwqg b;+3)3 yetion of transverse waves along the string?

A wave whose wavelength is 0.500 m is traveling down a 500 m long wire whoseyd2 ;w vg+6 tp(c00erm)kw1sfy1zc qz total mass s0fz my2 wqtc 10;pkged1( c zr+6)vwyis
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 aynen 8h4kw 4mdae*fol568ty ) transverse wave on a 2.0-m long string fixed at both ends is 200 m/s. Whd h8a w44ky)ome e86ft ln5*nyich one of the following is not a resonant frequency of this string?

  If a guitar string has a fund 22dgllo h:rn q:7w2m(b ayza0amental frequency of 500 Hz, which one of the following frequencie ya2rnblda7202: :mqw (gz lohs can set the string into resonant vibration?

  A stretched string is obseusorhc5tc ff30 i53l;d/:xzerved to have four equal segments in a standing wave dr/hi:;z3 cxurc f 5ostldfe 350iven at a frequency 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 ez f-0 o2v3e ;u,kfsopstanding transverse wave pattern containing 3 loops. What frequency is needed if the standing wave pattern is 3kups,; ez -2ffo ve0oto contain 4 loops?

  A string of linear density 1.5 g/m is under a tension of 20 N. Wh7dzdktt9h/ijge- + a,at should its length be if its fk, z7ah/e g9+i-dtjtdundamental resonance frequency is 220 Hz?

  Find the first three harmonics of a string of linear ma/gtuo.uw4gjn4/ ql d :ss density 2.00 g/m and length 0.600 m wojugn.l/gdu wt4: 4/qhen it is subjected to tension of 50.0 N.

A string of length 2.5 m is fixed at both ends. When 8lhg8 cptv-ta+akk,av /g 7;cthe string vibrates at a frequency of 85 Hz, a standing wave with five loops aac8+ph v lttkkca8,7/ g;-v gis 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.