The time for one cycle of a periodic process is callyn t(rb0sg b/.nrm2i7ed the

  For a periodic process, the number of cycles per unit time is called th 2-o1s ia*qo(cn 63ercuau2x agxe0; se

  For vibrational motion, the maximum w:q nt -e4h)ygvp.pknsf1 :p)l-8o oodisplacement from the equilibrium point is called thepsn-)o4ol v :wqp-nt ) ef 1h.:g8oykp

  A mass on a spring undergoes SHM. When the mas 4n2y(-(fe* e caihqrwd ll/b5s is at its maximum displacement from eq5eh*w/bef( ydl 4qn il-cra (2uilibrium, its instantaneous velocity

  A mass on a spring undergoes SHM. Wha.ibg ri ;w6)oin3f0v en the mass passes through the equilibrium position, its instantan.rwiif gba)03; in 6voeous velocity

  A mass on a spring undergoes SHM. When the mass is at maximu 9i*hzo5r e.aqm displacement from eqero9 i5*hz qa.uilibrium, its instantaneous acceleration

  A mass is attached to a vertical spring and bobs upbd1l.g kq82qyxp :c;e and down between points A and Bdl21g:yqp x.qkc8;e b. Where is the mass located when its kinetic energy is a minimum?

  A mass is attached to5hzf4;*is8 il iguay* a vertical spring and bobs up and down between points A and fyiui s45hlzi8g; *a*B. Where is the mass located when its kinetic energy is a maximum?

  A mass is attached to a vertical spring and bobs up and down betweedc *22*zghx4a 6rjuman points A and B. Where is the mass located when its pote2r*c62ua *jxm hg4d azntial energy is a minimum?

  A mass is attached to a vertical spring aw.x2lam/m3 sujm ob;24f s 0ognd bobs up and down between points A and B. Where is the mass located when its potential energy wm2/u ;j3 axf.lbo m 4ms0sg2ois a maximum?

  Doubling only the amplitude of a bn,a-tt2)j2n k 1zg8rij06 si2j hhvevibrating mass-and-spring system produces what effece)gt-vn0jn t6jzk 1 2hriji2a h82 ,sbt on the system's mechanical energy?

  Doubling only the mass of a vibrkr4 z rcry(50vating mass-and-spring system produces what effect on the system's mcr40 vrkz 5(yrechanical energy?

  Doubling only the spring consta;xwnu +1t z8pbq7y- t wa06mp2qpo2wlnt of a vibrating mass-and-spring system produces what effect on the 18-wp6 2 numwtp+qa2qty;p7ozx0lwbsystem's mechanical energy?

  A mass oscillates on thd+a 5t .ncakf5kd*d+ tsb ryhivb o3n 9(19(kve end of a spring, both on Earth and on the Moon. Where is the period the greatesttvhd 3 5( vbbs *9i95y.noatf(1kardd+kn+ ck?

  Increasing the spring constant k of a,k*ew h qbxf./out ku.w8qi dte:s8 39 mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the sysf8 */ t eqqwkx.wk39ei. u,8:stuobhdtem's mass m.)

  Increasing the mass M of a mass-and-spring system causes p5x4gwf ezb2i. 4l-ih* t x-59nvlxxe what kind of change in the resonant frequency of the syz5-i* b24xtpgfh lw9xi5n l e4e-xx v.stem? (Assume no change in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spring system ;+wb-ch9an. (8:rk.cz grkgz+ bomyrcauses what kind of change in the resonant frequency of the system? (Assume no other ch+g9o:ra+zr-; cwbz(nkkc r hg.my8b.anges 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 attachedhu89:nf nr) j- ql7lll to a weightless string of length L. For this system, when undergoin:7 r )j9llfhn8lqlun-g small oscillations

  When the mass of a simple pendulum is tripled, the time required for 1c x 7a ex9be2jj)vvo n48l/kmone complete vi ven9bm/ vla1xck8jo7)j4 x2 ebration

  Both pendulum A and B a(8h3 d0eqzm: g-jq/lbc c2q dure 3.0 m long. The period of A is T. Pendulum A is twice as heavy m0q:( 8qq/-hl3 e c jcdgbu2dzas pendulum B. What is the period of B?

  When the length of a simgacqpa/6 ; dm6t9tc,dple pendulum is tripled, the time for one complete vibration increases by a facto qatp mc;96tag cdd6,/r of

  What happens to a simple pendulum's frequency if both its length and mass are ingtqw l;g1c9o4 zae 8q;creasee;q;c8 gq9oglaz 41twd?

  Simple pendulum A swings bac4 s wh0m,jx 3smalr5k+k and forth at twice the frequency of simple pendulum B. Which statement is cam x+ljm0 k r3sws54h,orrect?

  If you take a given pendulum to9v/b*j z suhv( the Moon, where the acceleration of gravity is less than on Euh bv9(vj*s/zarth, the resonant frequency of the pendulum will

  Curve A in Fig. 11-1 re4bz lf1ah*7ia presents

  Curve B in Fig. 11-1 represents6x0upgc 4 8x86u1iwd q wano: .t 4ad7sbhvww;

  Curve C in Fig. 11-1 represcz ,.) smvr og0yiat.nex;()gents

  For a forced vibration, the amp)a*ub i:i.s nhlitude of vibration is found to depend on the

  In a wave, the maximum displacement o5r msq2r wa/z8f points of the wave from equilibrium is carz8sq r2m5/walled the wave's

  The distance between successive crests on a wave ih :s 5-6q(-ftl mltprts called the wave's

  The number of crests of a wave passing a pop3k/ rmu,hbf 44/3wk/ofeul s int per unit time is called the wave'sfkf3,/lku44h ur w3 ems op//b

  For a wave, the frequency times the wavelengtaq0 1t;gel,ys h-wz3g7mgr o9bz --pwh is the wave's

  The frequency of a wave increases. What happens to the distv fy7of +s,0piance between successive crests if the speed remains fo70,fv pyis+ constant?

  A wave moves on a string with wavelength l and frequency f. A si2- r; vrm,zalecond wave on the same string has wavelength 2l and travels with the same velocity. What is the frequency of the second wavz-;l2 m, ivarre?

  Consider a traveling wave on a stozidx: aa0.f c+5e or6ring of length L, mass M, and tension T. A standzo:ed+i 5o r .xfc60aaing wave is set up. Which of the following is true?

  A string of mass m and le +5z kq-ugt kwai1lu0k;soirm 5)9;dhngth L 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 mh+lts;d10-5wk gkoi kz)iuq 9a; 5ru mass of the string is increased to 2m, with no change in length?

  A string of mass m and length L is under tensio zp 6cflq )jn0yho8rk(hm 1,5rn T. The speed of a wave in the string is v. What will be the speedh(j,nmyqkc60 rfr )5lz8p1 ho 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 Tp c v-68*hpygw. The speed of a wave in the string is v. What will be the speed of a wave in the string if the teng6w *yhp pcv-8sion is increased to 2T?

  In seismology, the S wave is a transverse wave. As an S wave travels through ty6:f-nz)u lj*rjc:d qhe Earth, the relative motioz*rju-n): fl 6qdjyc:n between the S wave and the particles is

  In seismology, the P wave is a longitudinal waveuon6meosi - 95)y rtz6. As a P wave travels through the Earth, the relative motion o5snu)yet- m6 ior6z9between the P wave and the particles is

  The intensity of a wa,zhsdzmqr8f;p - */ql ve is

  A wave pulse traveling to the right along a thin cord reach(6: duog: aqxjes a discontinuity where the rope becomes thicker and heavier. What i:jodg qu( 6:axs the orientation of the reflected and transmitted pulses?

  Two wave pulses with equal positllo nk+lrff8)qm48- vive amplitudes pass each other on a string, one is trav-rflql+8 kmf4l8 )nvoeling 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 pass each other on a string. The one traveling toward the rphpb+2c2) nvly; h7yjight has a positive amplitude, while the one traveling toward +v hy;cp7bn 2)ly2pjhthe 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 strin7q-.fxgs r:s2dzs7oo+ ) rexm(n qe k.g fixed at both ends, occurs when

  If one doubles the tens24 i6 j0kj:zkixlusc (ion in a violin string, the fundamental frequency of that string 4cizxu si:260k( jjlk will increase by a factor of

  What is the spring constant of a spi yz79-9y)pwv:q/cmvqs-g me ring that stretches 2.00 cm when a mass of 0.600 kg is susp9 v7gq)mq:e s-y /p vzy-wicm9ended from it?

  A mass is attached to a spring of spring constant 60 a fxc).jzn 0b3N/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 oscillzxan3b 0cj f).ating. What is the amplitude?

  A mass is attached to a spring of spring constant 60 N/m along a r1pm wydi).cwg7 ,t* mhorizontal, 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 god1yc.)w7m ,wr*ip mgt back to its equilibrium position when it is oscillating. What is the period of oscillation?

  A mass is attached to a sjre+clj*l b (3pring of spring constant 60 N/m along a horizontal, frictionless surface. The spring is initially stretched by a force of 5.0 N on the mass and l3+l(jj *crle bet 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 oscillations incik/vi*8 -1e zf6hqb( 7 vxcos 5.0 s. Wha 1(zvsv/8x i*coqfh- 6i7k cebt is the period?

  A mass vibrates back and forth fu a;)opd a (byjay+lmz,.9 xk*rom the free end of an ideal spring of spring constant 20 N/m with an amplitude of 0.30 m. W,oku*;apj()y + a. mlzdxb ya9hat 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 sp jy -+:0,jv/ tkklfyrxring 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 equilibrium position. What is the total energy yy,rj/tk0xjvf -k+ :l of the system?

  A mass undergoes SHM with amplitude of 4 cm. T,j6gdc tki0hlmwlp 0r+ 7 m9q /okus30he energy is 8.0 J at this time. The mass is cut in half, and thedi6w0m0 o kj+ ru, cq0sk l7thl3/pgm9 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 attachh w8dux8he/6k;q +juced to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The obje;he6h+u wu j/xq88cd kct 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 of6b lqcte1v. *8ejbp(j spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple hablj6 e8vj1 .(p*cqte brmonic 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 the same?

  A 2.0-kg mass is attached to t.-2b61pnkogk 4 exde3pwdk )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 me d.4noew12pp6)k3d -bkg ktxechanical energy of this system?

  A 2.0-kg mass is attachedhy 12lf y9 nrj3suahtaro7*up0zz h*j) /p1:d 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 energrpza:ftsrupuhn d21h 3/l y*o*jya)1j 7zh09y of this system?

  A mass vibrates back and forth from the free end of an idey wm59k -58l;d*bh e9a falxhsal spring of spring constant 20.0 N/m with an amplitude of 0.250 m. What is98*y w5kb5aam d llh9e -hf;xs the maximum kinetic energy of this vibrating mass?

  The mass of a mass-and-spring system is 4pn*dd ni.5 ,v6xohu bdisplaced 10 cm from its equilibrium position and released. A frequency of 4.0 Hz iso v nn5idd6.*4 xp,hbu 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 sc np0v)++m g3zgk sn7kpring of spring constant 10 N/m. The object is d+ cvmgk)zng 3k+p0ns7isplaced 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 connle7y m .dr(-u;9p ygistant 10 N/m. The object is m(. ryl9-7yuipdeg ; ndisplaced by
5.1 cm from the equilibrium position and let go. What is the frequency of vibration?

  A 2.0-kg mass is hung fromcxbkwlc*5b-4 bt:.xv i,/e f j a spring of spring constant 18 N/m, displaced slightly from its equilibrium position, and released. What is th t5j i4vwblxcb*ckx,-f : b/e.e frequency of its vibration?

  A mass is attached to a spring. It oscillates at ay ywty3o7p)h o d(2r)dp.uw6 w frequency of 1.27 Hz when displaced a distance of 2.0 cm from equilibrium and released. What is the maximum velocity t3 hw6 72ydywdp)p)y.w uroo (attained by the mass?

  Two masses, A and B, are attached to different springs. Mass A vibrates with ax9oloop j,(3jfk69q d mplitude of 8.0 oojd3o,9q(k flx p6 j9cm 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 of B?

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches t/lypp(xy jfm (jsnn:zl4l 050 he spring 2.0 cm downward. The mass isnj (m p l0y0p4fln5x/:jzl(ys 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 suspmko.z7 5tousw8 3: emhended on a spring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is thzeh3 8mu5 t:ks mo.wo7en 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 suspended on a s oi.8kpgscq.lglk5mjn 74 t./pring. In equilibrium the mass stretches the spring 2.0 cmlo 4n 7g8l m..tsgijkpk c5q/. downward. 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 harmeh,tpjv -n89x onic motion obeys the following position versus time equatneh -t89,jx pvion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the following positr;scw4as 64,qjo 0 bj)b cbqr.ion versus time equati4a ,wb. 4j qq0r;b )bcjosrcs6on:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys th b: xlmyu7se8,.datvi :7;oihe following position versus time equayi7l: 8 :bu.7 dhveam isto;,xtion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes simple harmbir4zqp0/6l,o s l6hdm+eq 5f ;oswc-onic motion according l;s, c q owz5- /6 piloher64+b0msqdfto 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 forphs fob23lx5(ce constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the mass is released from rest at x= 10.0 cm.l3(x o5h sp2bf (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 h-:h bj*.deu ewb:s5g and perisb*b- ed 5.g j:h:ehwuod on Earth?

  A 3.00-kg pendulum is 28.84 m long.m, k wktp 6tzr4w6mm5kcby kg.l 6*s(- What is its period on Earth?

  A pendulum has a period of 2.0 (5up4 vl 5b1bai itxri05g jm:s on Earth. What is its length?

  The pendulum of a grandfather clock isur;.jq0s) )yl5jep-k/bz hez 1.0 m long. What is its period on the Earz/yselkj)q0-5u ; ezrp.h)b j th?

  The pendulum of a gr51c *d1cqvddge0rw y0 andfather clock is 1.0 m long. What is its period on the Moon wh1y0r wedqdvc51*cd0 g ere 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 a massless gac ,tzt vieh.68g+f,u * tuoeh1*js)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 v6o sghtj8th,*e+u., eg)it1z fuac* diameter sphere) had been attached to the string instead?

A simple pendulum consisting of a 20- vghhx;/,yf9b3qt;w1 fna a6a g mass has initial angular displacement of 8.0e. ayxafantw,3 h9g1b; 6 fv/;q hIt oscillates 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 v/+.u-rnf g xc0aj+ (kfw9jhl wave at a given time. The frequency of the wave ijl9a+x n /ukhw.0+ g(jv f-fcrs 120 Hz. What is the amplitude?

  Figure 11-2 is a "snapsc y4d cra-5b ta,7 kfowo;p0l7)jalg0hot" of a wave at a given time. The frequency of the wave is 120 Hz. Wha,4kyajfct7o0b pwg; lo a-) 0crdla57 t is the wavelength?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frequency 2:k;x9oxatrcof the wave is 120 Hz. What is the wave a9:rk2t xocx;speed?

  What is the frequency of a wave which z(oxd iak 7ayh2b fwv(b0;;d. has a period of 6.00 ms?

  What is the period of a wi2 svfpqu 1pfc )axfw1 5ei)k3f)3w9 tave with a frequency of 1500 Hz?

  What is the wave speed if a wave ha*) lgbvv9db:jy,/a h3tk1owzp3/fsds a frequency of 12 Hz and a wavelength of 3.0z:h dvdpab,3k ftby */lg1wj/ os)39v m?

  What is the velocity of a wave t0jgzy ;fdugaa8mn+f/ pio3) )hat has a wavelength of 3.0 m and a frequency of 12 Hzf+oaa)8pmzygu0 d;jn/g i f3 )?

  What is the frequency of a 2.5 m wave traveling at 179p- fl(/rxxw2niw f x y3ftr p(s3o6e400 m/s?

  A piano string of linear mass density 0.0050 kg/m is under a tension +ahqbg;)dy83q9z9ab v8 fajj of 1350 N. What is thh abf99;+ 3 zjgj8qa v)d8qybae wave speed?

  A string of linear density 6.0 g/m isuavj* rt2.1f :od i 8z4xjs/id under a tension of 180 N. What is the velocity of propagation of transv/dxja rz*o j2vt 84.:fdsui1ierse waves along the string?

A wave whose wavelength is 0.500 m is g;kybjs e 3a: 4lo9i7.v7vn5xy c0q rjtraveling down a 500 m long wire whose tota74 v 53ac.:yb;qlkre7j g9 xj onsyi0vl mass 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 propagation of a transverse wave on a 2.0-mg5g ri99e ymkmn6) *rz long string fixed at both ends is 200 m/s. Whi*i9nermgk5yg)6r 9 z mch one of the following is not a resonant frequency of this string?

  If a guitar string has a fundamental frequency of 500 Hz, which one o /jeyzwg;t*c/ f the following frequencies jz/g/e c*; tywcan set the string into resonant vibration?

  A stretched string is observed to have four2;vp61hrxu e pnqr) a+ equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a stahrn6e+1u a)qxpvr;2 pnding wave with five equal segments?

  A string, fixed at both ends, vibrates at a frequency of 1/rv fev2hnz:9er u8n42 Hz with a standing transve2enr/94 rh ezf8v:un vrse wave pattern 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/yjx 5qr6,s0 awm is under a tension of 20 N. What should its length be if its fun arswqx0j, 65ydamental resonance frequency is 220 Hz?

  Find the first three harmonics of a string of linear mass denz hfrbe em6 s*,g:c srd-x-k)5sity 2.00 g/m and length c5*zhkr)ef -rxbe :6dsgs m, -0.600 m when it is subjected to tension of 50.0 N.

A string of length 2.5 m is fixed at both ends. When the string vibrates at a wn8zefeq+nw6w u 017l frequency of 85 Hz, a standing wave wnwuew10 q+l8n wze7f6ith 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.