The time for one cycle of a periodic process is called syv+ t.(xds4fmxdy0; .-k vihthe

  For a periodic process, the number of cycles per unit time is caukv32 nz8j+snx16s zw lled the

  For vibrational motion, the maximum dispyr(c)kbgo 2p/ms q3l zxo/93ys+p tx)lacement from the equilibrium point is called tgcsblx m)syoyxz3(2 k rq/ 9p tp+o)3/he

  A mass on a spring undergoes SHM. .-yeojv: szgl ,n5+riWhen the mass is at its maximum displacement from equilibrium, its instanta-o.+lg ,:syeijr zn5v neous velocity

  A mass on a spring undergoes SHM. When the mass passes through thf6dxs6:c:de b e equilibrium position, its instantaneous veloddb6f:6cs: xecity

  A mass on a spring undergoes S;wzla(ga j)ypt nl,9 *HM. When the mass is at maximum displacement from equilibrium, its g;az wnt(l a*,jlyp) 9instantaneous acceleration

  A mass is attached to a vertical spring and bobs up and ; z2xz0u0be8, 1qwnm6ui/7xcia ycll down between points A and B. Where is the mass l yamqx/1zx; z wue ibcl6 ,8n7uil0c02ocated when its kinetic energy is a minimum?

  A mass is attached to a vertical sprinrccmalglrwi. t-td+vc j.(8nn/ 6-1 cg and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximumc d1r8(/ncgticw m c.nr 6lja. t+v--l?

  A mass is attached to a vertical spring and bobs upbo2ww9y nz56r)t-4l swq+ huwlb*qk( and down between points A and B. bl 2w u4n*)9htlwko b-56+srz wwq( yq Where is the mass located when its potential energy is a minimum?

  A mass is attached to a vertih)9vb(0f oom/(x;a xxwzzjk/ ts0 ua7cal spring and bobs up and down between points A and B. Where is thez70h(9 afo x(atxkbsu)/zx0/m vj wo; mass located when its potential energy is a maximum?

  Doubling only the amplitude of a vibrating mass-and-spring system produces what34ofyfeir(ufn . q3a.2 oae6x effect on the syseir eu4.qfy.33(an aof6o 2fx tem's mechanical energy?

  Doubling only the mass of a vibrating mejnvd2 p3z4a,7 jzp5kass-and-spring system produces what effect on the system's42, pj ja5evp7nzzd3k mechanical energy?

  Doubling only the spring 0ou95zl x ((wsdoqptea /5m32mh2ahh constant of a vibrating mass-and-spring system produces 02a/9haozhstl3w qhop m5u2me ( (5dxwhat effect on the system's mechanical energy?

  A mass oscillates on the end oft*bf3le *a /hz a spring, both on Earth and on the Moon. Where is the period the greatesa h*3*ltbf/ez t?

  Increasing the spring constant k of a mass-and-spring s pn*+pk 2lw)0lsfv2ngystem causes what kind of change in the resonant frequency of the system? (Assume no change s0 *lpwgk22)+npfnl vin the system's mass m.)

  Increasing the mass M of a mass-and-spring s8/xva1 payhi:5 v: 8toq kvif7ystem causes what kind of change in the resonant frequency of the system? (Assume no change ixpt hqafk7i v/yvo:v:1 8a85in the system's spring constant k.)

  Increasing the ampliy4 :j*yhkf d5jkwge0/tude of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no otk:h j4y5wek/j0gf d*yher 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 consis z-x.(dvevv5 mts of a mass M attached to a weightless string of length L. For this system, when undergoxd5( mz evvv-.ing small oscillations

  When the mass of a simple pendulum is tripled, the time required for on.n;w (kq3(:jdpo1i3tbuvm rj e complete vp3rdb q;ituknmj13:j. o((w vibration

  Both pendulum A and B are 3.0 m long. The period of A is T. Pendulum Ap.3 cc+c8qz /hu( u )tyxcz17vxlyji9 is twice as heavy as pendulpx z tu8ulhycj31 7+c.c9yv/()ixcqzum B. What is the period of B?

  When the length of a simple pendulum is trd;l4zp:mu nq -l7j ;vgipled, the time for one complete vibration increases by a factor of -z; 4: 7dnuvjmqlpg;l

  What happens to a simple pendulum's frequency if both its length and mas.73vpr4/y*+ qzi bz+isx rm mes are incr3+4mm szz +v*x /rir.qpb7 iyeeased?

  Simple pendulum A swings back and forth at twice the frequency of simple pend3 w .(vsj8lzrfulum B. Which statement is correctw3l zsvr 8.fj(?

  If you take a given pendulumcym :fzlx;uyz5+9l6u to the Moon, where the acceleration of gravity is less than on Earth, the r6c +uzy95l l:yzu ;xfmesonant frequency of the pendulum will

  Curve A in Fig. 11-1 yl+5r h(0t2sioy:zm l represents

  Curve B in Fig. 11-1 r-g amk0p.atx9 epresents

  Curve C in Fig. 11-1 represent (6ok-wd l(e lbar6(ojs

  For a forced vibration,5j x y,sg2 sw69rlb9lz r.gxe6 the amplitude of vibration is found to depend on the

  In a wave, the maximum dis:7+ i7b r2s+iqve rgyrplacement of points of the wave from equilibrium is called th7rq+r: sv2ib7gri ye +e wave's

  The distance between successiz )2msa (cxuy8n*(rtgve crests on a wave is called the wave's

  The number of crests of a wave passing a point per unit timen *1 r qknmkgi.9oi7o( is called the wave' n7 iik.k(*g9rn1omqos

  For a wave, the frequency times the wavelength is t3kef69 h2u3r ei g-au nmhp02nhe wave's

  The frequency of a wave increases. What happens to the distance fsj/ 4j*+sykp between successive crests if thejp/ *+jy 4fsks speed remains constant?

  A wave moves on a string with wavelength l and frequencm-nez45f1 a4vrp r 2fby f. A second wave on the same string has wavelength 2l and45- 1rfb4eznf mvapr2 travels with the same velocity. What is the frequency of the second wave?

  Consider a traveling wave on a string of length L, mass M, andwlppq- , 9jlcm *q+w7x tension T. A stanm9*-j pq 7q wclwx+l,pding wave is set up. Which of the following is true?

  A string of mass m and lengzco.8lxy2ynvqn :j 25th L is under tension T. The speed of a wave in the string is v. What will be the speed of a wave in 22lxcqzonv njy58.y: 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.c1ca(xb:.6f+tp+5a twwbjc eimk tf;o49 g e, The speed of a wave in the string is v. What will be the tbf5 wb6+m ct,w4c .pi o1a+;e9jefx(ga:t kcspeed 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 u)gwv2rxp da3 fa-v q(r2t+j x2kj8cj1nder tension T. The speed of a wave in the string is v. What willcjafqj2gx21 r +trv a) wd-3p2(jx8vk be the speed of a wave in the string if the tension is increased to 2T?

  In seismology, the S wave is tjptsi.ar)-r y:xj7 s0hdp27 a transverse wave. As an S wave travels through the E axr.yjdis-70:)ttj hr7sp2p arth, the relative motion between the S wave and the particles is

  In seismology, the P wa.0yywb5s g 7489qvvauhom)vp1yh *nhve is a longitudinal wave. As a P wave travels through the Earth, the relah b nh1g8sayyvqvh 4vw9op y)*mu7.05tive motion between the P wave and the particles is

  The intensity of a wave is f9d n(,drdoh*3qmc9s

  A wave pulse traveling to tip (6a5mn 0hvtgc/aui2 noa,kd1t)4d he right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. na(1hp/6tvo,0c k)5mga 4uia d2tn id What is the orientation of the reflected and transmitted pulses?

  Two wave pulses with equal positive amp2 ,v 3z.u qba3fh5swx,pzn-bilitudes pass each other on a string, one is tr-xb zn5,i,v.sbawfhpu323z q aveling toward the right and the other toward the left. At the point that they occupy the same region of space at the same time

  Two wave pulses passa,tm3wmv.fi/ti4 spvo; 9 0 08hz btqe each other on a string. The one traveling toward the right has a positive amplit0aetvzif 0tvm .ho,/p bqwis9;483tmude, 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, such as a string fixed at both ends, occurs whenif9vq:fh bam0fhf1--bp4 u* r

  If one doubles the tension in a violin string, the fundamenm-.97i dzhsqx 3owi t)tal frequency of that string will iw -xdo t39)qi7zis .hmncrease by a factor of

  What is the spring constant of a spring that str wq0 gesu:a(h(t2xxs i9u*d j-etches 2.00 cm when a mass of 0.600 kg is s9d:0ueig ( uhj-x (a *qxtsw2suspended from it?

  A mass is attached to a spring of spring constant 60 N/m along a hoq1dibw :s5/,qj (fg vkrizontal, 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 itsq j1df5q/iw(: k vgbs, equilibrium position when it is oscillating. What is the amplitude?

  A mass is attached to a spring of spring constant 60 N/m alo wfaf nxg-f 4a1v6w+yvql(8f :ng a horizontal, frictionless surface. The spring is initia4 aqyxww8vf:f-l( vng f+f61ally 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 constannzx(+g3v2fw7hdr o yi 9y +;+lki*xyrt 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 taki+ +h7rx +zy;2fy3oxl*vknd9wigyr(es 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 unde-u 02.iwy y.sr. apyfxrgoes SHM. It goes through 10 complete oscillations in 5.0 s. What is th ufyy.yx 0rsp2-a..i we period?

  A mass vibrates back and forth 0 ,x 5hqqzius8piy52 ec )m+sufrom the free end of an ideal spring of spring constant 20 N/m with an amplitude of 0.30 m. What is the 2 uzi sqciux0,8m5+pqye 5)hskinetic 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 s l(ccqdsj .ea1y7k )s;pring 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 po d;jql.as7s1k ( yec)csition. What is the total energy of the system?

  A mass undergoes SHM with amplitude of 4 cm. The energy is 8.0 J at t.: tya(fdo ,ffhis time. The mass is cut in half, and the ,f f(.odyf at: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 attached to a spring of spring constant 20 N/ ;. pqahpo+c)u2yfed 9m along a horizontal, frictionless surfacuoe9ap)qf + y;cpdh2 .e. 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 along+*zepst l 8)ke 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 enert)zee8 k* slp+gy and the potential energy the same?

  A 2.0-kg mass is attached to the end r39ravv8i/ ce34bio/dm 1hbk of a horizontal spring of spring constant 50 N/m and set into simple harmonic motion wiom/84ib/vhe k1c da3r 3bvir9th an amplitude of 0.10 m. What is the total mechanical energy of this system?

  A 2.0-kg mass is attached to the end of a horizontal spring:6+b/ki q0 1we4z*ac xrccs -7 pzlwce of spring constant 50 N/m and set inwi /4 kclxec*+:q z67wpre0c-cbs az1to 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 ideal spring of spring 5;cvjhuete7idhau he6;c38ub9 7nu; constant 20.0 N/m with an amplitude of 0.250 m. What is the maximum kinetic energ juce7cdb ;nv85 hu;6i37he9uaue; h ty of this vibrating mass?

  The mass of a mass-and-spring system is displaced z8;brsxs0nv 210 cm from its equilibrium position and released. A frequency of 4.0 Hz is observed. What frequency would be observed if the mass had been displaced only 5.0;z8 sxvs 0r2bn cm and then released?

  A 4.0-kg object is atx;n: s9 y0+eoptd 8/uak u.iagtached to a spring of spring constant 10 N/m. The object is displace0ea+u9kati. u/:gnyod;ps x 8d 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 sprin i2+r2gz0e-ivm 1w:tfgt vw b/g constant 10 N/m. The object is displa:v-it bfr2/gzg i w02+me1wt vced 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, dhuyqib9q rp ,;8l-i9 oisplaced slightly from its equilibrium position, and released. What is hiu-8ql;p9ib9, qy rothe frequency of its vibration?

  A mass is attached to a springu9vroh0wo7) k . It oscillates at a frequency of 1.27 Hz when displaced a v)h 7rk 9oowu0distance of 2.0 cm from equilibrium and released. What is the maximum velocity attained by the mass?

  Two masses, A and B, are attached tc1hm83g8ak1u u q3 ehl(xli,z o 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 cm at a frequency of 16 Hz. How does the maximum speed of A compare to the maximum speed ofg1 h(1laq3zkim8,83el h uuxc B?

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass s48dmaml 3qx6vkj; 8v uxm7h6ptretches the spring 2.0 cm downward. The mass is then pulled an additional divxxavd4u m;m7 h6l86p3jkm8qstance of 1.0 cm down and released from rest. Calculate the period of oscillation.

  A 0.30-kg mass is suspended on a spring. In equh 7fp-1x +m4pp mss7vsilibrium the mass stretches the spring 2.0 p7vmm4 7+-h p pxsss1fcm 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.

  A 0.30-kg mass is suspende(6 / lo;x5yqg x, 5pjoh7vjv7tblca9cd on a spring. In equilibrium the mass stretches the spring 2.0 cm downwarg5vohxo cj(9 cpx7v6q,7l l j/yba5;td. 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 harmonic motion obeys the following position versus tik+ 2g k:7v2npijy7yl ame equ2:pg 7la27j+ k yknvyiation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion q06xj;zxovujmt . ( /d i (caeb261y;oetl0cbobeys the following position versus time equatmbz atyxcdu l0v.jqoi6ee;21 (j6x0bc(to;/ion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following position versus tixsx+0do- e6i:j4zrs8n u 8 vxzme equati:s 0+j6 zu nz es8x-4vxd8oxrion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a0wrixz/0o h.o spring executes simple harmonic motion accord/0 0 o.izxrhwoing 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-9dnx * 1fuzy8 jihtx7scillates on a horizontal, frictionless track. Atx78y xt dj f1hi-9zu*n 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. (a) What are its frequency a/ob 8))/ zweqvepttq;*zsp.ch s6l0d nd period o/z/op)*ds h . b z;pqweett68c v0q)lsn Earth?

  A 3.00-kg pendulum is 28.84 m long. What is its peryfkn19 l6/-i5allz s xiod on Earth?

  A pendulum has a period6 ei ac58c7nid of 2.0 s on Earth. What is its length?

  The pendulum of a grandfather clock is 1.0 m long. What is its perh ,hhemw (92ewl4gy,i iod on the Earte9(w 2g wih4e mhl,h,yh?

  The pendulum of a grandfather clock is oz9xhh 38lr5p 1.0 m long. What is its period on the Moon rzh h8xo 9pl53where the acceleration due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-kg spherical mass attachs60g6 a-j eey-mf8o5.yuoq1d g uamb1ed to a massless string. When the mass is displaced slightly from its equilibrium position and released, tfuqe 6muo8.1 dga0yb6 51se -j-omgay he 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 the string instead?

A simple pendulum consisting of a 20-g mass has initial angular displacem4g1c4xkd fn3h nv4i-uent of 8.0e. It oscilla4xu-gn 4kh143 nfci vdtes 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. Theyl 9dts y9* z: ne(l*bq-a.yfz frequency of the wave is 120 Hzyst y(9yf:9l. *qnal* -d ezbz. What is the amplitude?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frequency 2yc6nzy 0wmf0zlk5zylra a ,n.wb6:3 of the wave is 120 Hz. Whacy3w0a 5f20nzr,nmz zw6y.k a:llyb 6t is the wavelength?

  Figure 11-2 is a "snapshot" of a wave at a given time. The fi0bcfjqh/1v c ;s pn)2,ji7vvpdht60requency of the wave is 1206;7vhs0f/p2tbv1p jcc0 qj,)hidv in Hz. What is the wave speed?

  What is the frequency of n); vt+ eo6.quy wkb.0dekuu(a wave which has a period of 6.00 ms?

  What is the period of a wave(efz-b 1f1xq vi 9ly.q with a frequency of 1500 Hz?

  What is the wave speed if a wave has a fr 2x5q *gsmvemf:po(f+equency of 12 Hz and a wavelength of 3.0 m? pmf q5e2f+gv x:(so*m

  What is the velocity of a wave thaq g/ adg+sg)o0i5w2sit has a wavelength of 3.0 m and a frequency of 12 Hz a0)5/ssgwd qg+g i2io?

  What is the frequency of a 2.5 m wave traveling at 14007 a 8m9 w(f.b0vmapjhb m/s?

  A piano string of linear mass density 0.0050 kg/m f/*fu9gfnvv 7q lb eumcc 3)xcn.tz*6m(64p xis under a tension of 1350 N. pzlnv ( .x ecc34v/nmu 6fm cg**ftub9q6)x7f What is the wave speed?

  A string of linear density 6.0 g/m is under a ) zbmleeh(051tv1c6jvjb0 y wtension of 180 N. What is the velocity of propagation of transverse waves alon160jtz c )1v5jl v0whmbb(e yeg the string?

A wave whose wavelength is 0.500 m is tra3q m(pka pb.*ktwb:r ;veling down a 500 m long wire whose total mass isb 3wkp m(t*.rak q:;bp
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 long string fixm5b+dh mk-sts )a t4.)mtb s1 tthu/s:ed at both ends is 200 m/s. Which one of the followint+)mbb: t ms4duhksts-h) 51 tt s.a/mg is not a resonant frequency of this string?

  If a guitar string has a fun71oa )h y;rpdi4+xn *w4spi/i eoeta* damental frequency of 500 Hz, which one of the following frequenci**wi/aahp r4eoe+)psiy7indt o;1 4xes can set the string into resonant vibration?

  A stretched string is5fckhdp:jf7frjui s:tn in(* 8es8 20 observed to have four equal segments in a standing wave driven at a frequek(j2fj:isn8h: sfte 5 8fp 7n cu0rdi*ncy 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 12/0. 9lz4 3rud bkwnt zgs,fz+j Hz with a standing transverse wave pattern containing 3 loops. What frequency is nee.zjz/ wfzn 4 0d,s9+br tgulk3ded if the standing wave pattern is to contain 4 loops?

  A string of linear density 14 f3ocah6um3u.5 g/m is under a tension of 20 N. What should its length be if its u3o3cm u6h a4ffundamental resonance frequency is 220 Hz?

  Find the first three harmonics of a string of linear mass density 2.00 y5aq bx(dc7j27:ydlj;l rva- g/m and length 0.600 m when it is subjected to tension 7dal5 :vc jly2q; xy rd7-baj(of 50.0 N.

A string of length 2.5 m is fixed at both ends. When the+31o9uxv0ff yrwt 5e l string vibrates at a frequency of 85 Hz, a staow 5tl+efr093uy1xfvnding 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.