The time for one cycle of a periodic process is h -ppc 3)py)e:i8gzof nlms2,called the

  For a periodic process, thet5f8cew4 iw 5iyvhyc1lij68zp e-5d. number of cycles per unit time is called the

  For vibrational motion, the maximukvx32+4bg6 rs 0d1nj m p qh51kqgov,um displacement from the equilibrium point is called th4ho3sqxv+ 1b 1dqm2k5j0vugnr g6 p ,ke

  A mass on a spring undergoes S/ pxxxc:ykv3s ns)+a ng+nr 9kb2ac22 :hr*yvHM. When the mass is at its maximum displacement from equilibrium, its instantaneous 2 ) p:a:sca /gns9rvx2x2nkxyy3v*+ c hk+b rnvelocity

  A mass on a spring undergoes SHM. When the mass pa5 s icci5vqh2 e;s*w*asses through the equilibrium poi c;*ae s*5qwcv5h2sisition, its instantaneous velocity

  A mass on a spring undergoes S3o5ln.f r3mrbHM. When the mass is at maximum displacement from equilibrium, its instantaneous acceleratio3 mo53r.r fnlbn

  A mass is attached to a vertical spring and bobs up and down between points A:i: yh7bu:t9xqwr*q *xk)fs)9 y i8cb omfvb1 and B. Where is the mass located wxfhqqf burc vmiiw:y 9bt7*8by xs)1k: )* :o9hen its kinetic energy is a minimum?

  A mass is attached to a vertick*3+weztg el y2k. 4vq rl6oj.02o mihal spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maxi y *oom+0.ve.qg z64jlk rh2ie2wt3lkmum?

  A mass is attached to a vertical spring and bobs up and down betweeab i) uyg.2p-a 8lp1lroq 4xe:n points A and B. Where is the mass locate1rguxpa y)-4le. i:q8b 2lpaod when its potential energy is a minimum?

  A mass is attached to a vertical spring and bobs up and down betwer my /;(;zmiphen points A and B. Where is the mayrhm;/( pimz ;ss located when its potential energy is a maximum?

  Doubling only the amplitude of a vibrating mass-anx;,rylgu b+.we6kk3t)mvi :nd-spring system produces what effect on the system's mechanical en+3lmk w.,tnir x)k:uvb;ye6gergy?

  Doubling only the mass of a vibrating mass-and-spring system produces i p)c9fscw1sd qd9(p 0what effect on the system's mechani sp) cfw9q0ci9dsp1d( cal energy?

  Doubling only the spring cyn// .zss(xy m)kc* soonstant of a vibrating mass-and-spring system produces what effect on the system's mechas)zxmn(kc*/y. s/y os nical energy?

  A mass oscillates on the end of a spring, both on Earth and on the azyk3 cug6ai 2 7bhh; 2mn/y3aMoon. Where is the period the6iyamy2z/c7nhh b gk3 ;aa u23 greatest?

  Increasing the spring constant k of a mass-and-spring system causmt;q ueoz/sxnbnhh v3*- +6t 9es what kind of change in the resonant frequency of m *one/h39 u ; q+sx6ntvz-htbthe system? (Assume no change in the system's mass m.)

  Increasing the mass M o1a5o3yzs9fog6m n u, gf a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the s3,5s gu9n omyo16zgf aystem's spring constant k.)

  Increasing the amplitude of a mass-and-spr2-5 t:jb*q3pb 6hzdedl (e beking system causes what kind of change in the resonant frequency of the system? (Assume no :klhe-z e ped btq *3b2(j5b6dother 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 sy,,nz x9ki); dc,rnmrtring of length L. For this systd, iz r);cn,xnm9rk ,yem, when undergoing small oscillations

  When the mass of a simple pendulum is tripled, the time required for onedx8k8(r u7/4w/e,db wdws ydi complete vwwxi /d8bk sd/4deyd(r, w87u ibration

  Both pendulum A and B are 3.0 m long. The period of A is T. Pendulum A 0zqnkjoi frtv;(bzt i 3j-4/6is twice as he-n iv;t/i6or0 k q( zt3fj4bjzavy as pendulum B. What is the period of B?

  When the length of a simple pendulum is tripled, the time for one complete 3pa:li-nkmf1 3k1a2ig ung. * raq /uhvibration k-fuq 3i/r*n1gaa1l u23 aig nm:.khpincreases by a factor of

  What happens to a simple pendulum's frequency if both its len tl y( wkvn)fe.;z)ba)gth and mass are increw(ev t lkzn))y abf.;)ased?

  Simple pendulum A sw 0of0ur 6fciiges g;70ings back and forth at twice the frequency of simple pendulum B. Which statemeegsf0uiroif7c 6g 00;nt is correct?

  If you take a given pendulum to the Mo ql a;f1q4npgt3l j// moyo+5j/jzc .jon, where the acceleration of gravity is less than on Earth, the resonant frequency of the pendujq;4c / m3 a1 jog+ l/5ly/pqzfj.ojntlum will

  Curve A in Fig. 11-1 represents wp1q racv-)0r

  Curve B in Fig. 11-1 represen9j :sc8 oa gjugy, *2rbv1hw)kts

  Curve C in Fig. 11-1 represe(1 -qh sq8scim *q y72nzsqy8knts

  For a forced vibration, the amplitude of v2potz9k4 /6(qiia bhg ,7yz qyibration is found to depend on the

  In a wave, the maximum displacement of points of ,-8c+ 0v7ljclhvreow the wave from equilibrium is called the ove w8-,r+c7 j0hllcvwave's

  The distance between successive crests on a wave is called th16ngs/map 3qv4j: 7x,apjb tje wave's

  The number of crests of a wave passing a point per unit+:akk0l4(n 9 ex zwvta time is called the wave'0kw+l at 9:xvae4z(n ks

  For a wave, the frequency5demrpw4) .o v3z .dm,y yxzm/ times the wavelength is the wave's

  The frequency of a wave increases. What happens to thh dw2q( a9e,qre distance between successive crests if tqedw a9qrh2,( he speed remains constant?

  A wave moves on a string with wqdozcx ;+)7bw7 n+anx avelength l and frequency f. A second wave on the sax++7wao;nx nzcd b7 )qme string has wavelength 2l and travels with the same velocity. What is the frequency of the second wave?

  Consider a traveling wave on a string ofr4lt,ik-kw c8mi)ywo;a t85r length L, mass M, and tension T. A standing wave is set up. Which of the followingt8klrc-kawwi mo;y5r8 , 4t)i is true?

  A string of mass m and length L is under tension T. The speed of a wa ,oo +4zql8r bfdx9ey1aghq-2ve in the string is v. What will be the speed of a wave in the string if the mass yzlx982br 4fh+oqaqog-, e d1of 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 the 9kdu/ku xnozi 9un3bcd9o1i 7w)y7v1strinowkku7/u1ddiou37y 9v cin 9xn) 1 9bzg 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 che:08 dfdkcj-5/bjlis 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 the0lf8h- ck /5 eddj:cbj tension is increased to 2T?

  In seismology, the S wave is a transvz4qf:l// dcixerse wave. As an S wave travels through the Earth, the relative motion between theq/4xcl /f i:zd S wave and the particles is

  In seismology, the P wave ifboai1;v x;dq; za5q6 s a longitudinal wave. As a P wave travels through the Earth, the relative motion between the P wave and the para5a;;1do6x iqfvqb;z ticles is

  The intensity of a wave i/y6t ijpl xfud4 s2n)ndr;9e+s

  A wave pulse traveling to the right along a thin ci/l hg;rpj+v8ord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of tg/;vih rl +pj8he reflected and transmitted pulses?

  Two wave pulses with equal positive amplitudes pass ei de60/3onvmoach other on a string, one is traveling toward the right and the other toward the left. At the point that they d6im0 /voo ne3occupy the same region of space at the same time

  Two wave pulses pass each other on a string. The one traveling toward the rix6jj u g7znqkn71-v p)ght has a positive amplitude, whilenkjzux 71-njv 6qpg)7 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,n44e j 1yug6l.6s4sgj4zyto ,sc ex6 u occurs when

  If one doubles the tension in a violin string, the fundamentvjob:u;/lj j0 5 m3bmx4:gpqy al frequency of that string j/x 5bjmo3jbg40mqu :y ;v p:lwill increase by a factor of

  What is the spring constant of a spring that stretches 2.00 cmy (t(c0 k a2 fc6vgjfsyea1xm6, 9mm0y when a mass of 0.600 kg is 6my, gyyf0 2xc (sc6tkavjae90(1mmfsuspended from it?

  A mass is attached to a spring of spri9oapx*t zk8wr(e,x0 b ng constant 60 N/m along a horizontal, frictionless surface. The spring r(0opa x,*z9w b8txe kis 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 amplitude?

  A mass is attached to a spring of spring constant 60 c**5hue( :a l ah7hmxxf1uk(w 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 ghkm(ax5lx* *a7(h :uuh1 ecfw o 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 horizo51dowoypo3 qdh/24,i igg*o y ntal, 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 wheo4iygoq3, oy1d pi /o5d2*w hgn it is oscillating. What is the frequency of oscillation?

  A mass on a spring undergtc 6l gf*esazsplt711 xx43c;oes SHM. It goes through 10 complete oscillations in 5.0 s. Whatt x s ecl7zx;1p1ft3c4sga6* l is the period?

  A mass vibrates back and forth from the free end (u*4twcjosjt 0h6zsl( 5c;pp of an ideal spring of spring constant 20 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 po6c( *jpzuw tjshp t4l0s5( ;cosition?

  A 0.50-kg mass is attached to a spring of spring constant 20ih,(bq4k ik, d 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.i,,dihkq4k (b What is the total energy of the system?

  A mass undergoes SHM with amplitude of 4 cm. The energy is 8.0 J at this tim:4kzqukdg /.pbcr+yn4e5eh6f .. j oie. The mass is cut in half, and the system is again set in motion with amplitude 4c: .6 bhk.iroj4 /zk5gpe un+ yfe.4dq.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/mkbm2xop1 * y8w along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed ofmy8 1wk* 2xpbo 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 sprinc j/s-.1( wi b5+2s xej)d;ofetv oetyg constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a spej5 ct+b;y(t ejxs-1i/f e2.o ow)vsde ed 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 endh (e2bpfb tpfuoq 21.-nc(m5 c 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 o ot-mn pfp( 5.(b 2uq1efbcc2hf this system?

  A 2.0-kg mass is attacg ngx2/ ek8ak21jjo8ehed 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 mechanical energnexej a12/8g kjo2 8gky of this system?

  A mass vibrates back and forth from the free en)kj3mcl* a d7aq3cl j+bf9 2fud of an ideal spring of spring constant 20.0 N/m with an q9u j +)ja a2f cfblm3d*3c7lkamplitude of 0.250 m. What is the maximum kinetic energy of this vibrating mass?

  The mass of a mass-and-spring system i6kd gx,+kqjw ieg+*n /s displaced 10 cm from its equilibrium position and redg++k6* x/jnwk,ieqgleased. 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 jz,kes pi-eb1,mb 6(xa spring of spring constant 10 N/m. The object is di bx,-iemkb(pszj e16, splaced 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/mlez(;gw4zwhsr c4;s8. The object ishrw4; 8s(z;zwg c4sle displaced by
5.1 cm from the equilibrium position and let go. What is the frequency of vibration?

  A 2.0-kg mass is hung fxqoi64;+aoc k7mr6 aqrom a spring of spring constant 18 N/m, displaced slightly from its equilibrium posi kc4q6m;6+7ixraaq ootion, and released. What is the frequency of its vibration?

  A mass is attached to a spring. It oscillates at 96s-i7abwwt r a frequency of 1.27 Hz when displaced a distance of 2ib9 -rw6wta 7s.0 cm from equilibrium and released. What is the maximum velocity attained by the mass?

  Two masses, A and B, are atvhug: ,oc3 /ldtached to different springs. Mass A vibrates with amplitude of 8.0 cm at a frequency of 10 Hz and massu3/l,dv c hog: 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 equilibrf 99zgsux+pdp z,z- a(ium 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 op zs( gxd9puz-z+f ,9af oscillation.

  A 0.30-kg mass is suspended on a spring. In equilibrium the ma(fgvgdgjz- xh5/ 9l dh2+v pq-ss stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. Caf q2g+vg-59/-h dxjhvzgd pl(lculate the total energy of the system.

  A 0.30-kg mass is suspended on a v8)m-1sb*ri 5ms8 qslxhbf q.spring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass isq bv)88mxs*hqsfr1bm5 . lsi- 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 f;( k)veoc tpa2ollowing position versus time equa)2ocvk( p;t aetion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion 5 z,uo h nx,h*3e.yd79vwl :k(fgfjjxobeys the following position versus time equf gx n3 *jh:vodulhz 7e,j 5fw.yxk,(9ation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following position;nuppx1 2nll c1:ewqpi x+6 t0 versus time equat+p : pplql1e ntwci12nx6;0uxion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes simple harmhq(kdm:if0q98 1dc uk onic motion according to t8idcd:khf(k 1 qqmu09he 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 fohs494 +f x+z7p/vt4c ugcs byyrce constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the mass is releau4 7gvy c4h4/cs+xb+stzyf9p sed 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 a(ng6uejff-mn;q6 -(t dc z;w/b o3pfvre its frequency and period 3fbpu (cm6e(6 of/v;f- z;-qwt djnng on Earth?

  A 3.00-kg pendulum is 28.2aq9kx(v ..deqk;ll ih-zs /o84 m long. What is its period on Earth?

  A pendulum has a period of 2.0 s on Earth idn8psh -xyae5zw192. What is its length?

  The pendulum of a grandfather clock is 1.0 m long. Wtx3pgq/2i7v8is6rkz hyhxm i j 25f0 .hat is its period on the Earth i i823 2h im/skx5jv.yprgq6 7thxz0f?

  The pendulum of a grandfather clock is 1.0 m long. What is its period on t 9u3dn:h sn,iehe Moon w,:i9hseu n3dn here the acceleration due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-kg spherical mass attached to ri-// 9zj4xrx8 csb vqa massless string. When the mass is displaced slightly from its equilibrium position and released, the pendulum swings back and forth with a freq9xix/ rsz4/bc8j-rvquency 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 dispq,v 6rm yaf4;elacement of 8.0e. It oscillates with ,ay4m;erq6f v 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 give0maix tj m6. ,.etwcw,v4s5o tn time. The frequency of the wave is 1 .w.sxit4oej mc06at,t m,v5w20 Hz. What is the amplitude?

  Figure 11-2 is a "snapshot" of a wave at a give w7)s* zyadf-gn time. The frequency of the wave is 120 Hz. What is the wavelengthya*s) dzwg-f7 ?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frequ;xv0w4q ehn* iency of the wave is 120 Hz. What iqhi vxn w;*0e4s the wave speed?

  What is the frequency of a wave which has a period of 6.00 mszbfhit1u d7 b, k7osk- /5v(rm?

  What is the period of a wave with a frequency khq73pp 0ie0cof 1500 Hz?

  What is the wave speed if a wave has a frequency of 12 Hz and a wavelendlxm;3w /o grpa/z3i-gth of 3.xi/m gz3 -rld; 3awpo/0 m?

  What is the velocity of a wave that has a wavelength of 3.0 m and a frequed9r4yd(j;srx fm 4jz(ncy of 12 Hz?jx;y 4r j4f( rdzsm(d9

  What is the frequency 7* g1lj31 dz,l-axpm axgy;y jof a 2.5 m wave traveling at 1400 m/s?

  A piano string of linear mass density 0.0050 kg/m is under a tension oib2m6;7m hdeq f 1350 N. 26idmmh7;bqe What is the wave speed?

  A string of linear density 6.0 g/m is under a tension of 180 N. What is the v2 fu6 fr6s2y ckrd*ufq)e0ac5m/wn h 4elocity of propagation of transv5m2urfs e* /)h4rcq6 kcf fnwa2 6d0uyerse waves along the string?

A wave whose wavelength is 0.500 m is tratto.oq2 k c q us;2k0dl0lho./d b,k3zveling down a 500 m long wire whose total mass ic.3. ;l0ks dzthkou,oq/l d k2bo02 tqs
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 stri2*zi)h;p c skwng fixed at both ends is 200 m/s. Which one of the following is not a resonant frequency of this string?;piw*2 )skczh

  If a guitar string has a fundamental frequency of 500 Hzo: 1f +mqem3kog. ,vae, which one of the following fgvq eo,m1+a f3kem:. orequencies can set the string into resonant vibration?

  A stretched string is observed to have four equal segmew92 ddv0 yab1yr*j5es*)iem hnts in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wavs*jr 5 9y)mdhw2vey*1ib a0ede with five equal segments?

  A string, fixed at bothej4yh)6b;we y ro*ch3 ends, vibrates at a frequency of 12 Hz with a standing transverse wave p; h)*e oc6hw3rybje 4yattern containing 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 tensio/2dx.nad ct7j n of 20 N. What should its length be if its fundamental re j/72 cnxd.datsonance frequency is 220 Hz?

  Find the first three harmonics of a string of linear mass density 2.00 )fdx7;.rijrm6bwmu,w yrp 14g/m and length 0.600 m when it is subjected to tension orf.mp,r i;)bu mwxy67d w1 r4jf 50.0 N.

A string of length 2.5 m is fixed at both ends. When the string vibr-wby l wo)xz9e*z6 gs9ates at a frequency of 85 Hz, a stw)z9zwx6g ylbo- e9*sanding 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.