The time for one cycle of a periodic process 0xtbeu1fn;-k4s0 b vfwv/ s/yis called the

  For a periodic process, the number of cycles per unit time is calleqbd9fu,w.nv du +7wo2,k q3r6sxz+ yyd the

  For vibrational motion, the maximum displacemre.yd6zq1 wr uoova. y a3*3o(ent from the equilibrium point is called 3 aowye ya.z. do(1r3u *6rqvothe

  A mass on a spring undergoes SHM. When the mass is at its maximum diszf ajki6 -ly(m zyh,,*placement from equilibrium, ayjy l( z6fh*k-miz,,its instantaneous velocity

  A mass on a spring undergoes SHM. When cc:jj;*ap:i,(0pa hjmpo /es0vbgm0 the mass passes through the equilibrium position, its instantaneous veloci0mm*jopp(gbae/ pvics jj:,h0;a :c 0 ty

  A mass on a spring undergoes SHM. When the mass is at maximum displacem fp2gw kpf 3c1nxzxv8(v) s:2zre.4 ekent from equilibrium, its instantan 3)pv.neexfck4 8zzs2 f:gp1(kr2xvweous acceleration

  A mass is attached to a vertical sp31y2r4 cph tu258 5af5 gvh)xiqplj yzring and bobs up and down between points A and B. Where is the mass locl q rzahyf5g15x4j2)pcpy3tv u25 h8iated when its kinetic energy is a minimum?

  A mass is attached to a vertical spr:+9qp 0v5 ihlf agnb-uing and bobs up and down between points A and B. Where is the mass located when its5hupibq 9n+- vfl0a:g kinetic energy is a maximum?

  A mass is attached to a vertical spring and bobs rb,xc3v8qsi ) up and down between points A andcs8xvi3bq)r , B. Where is the mass located when its potential energy is a minimum?

  A mass is attached to a vertical spring and bobp; nuh;.j umynwcdinp 5n; 4s ;7l8hz5s up and down between points A an jp 5hmy; insl 5czuwn7n4d;.nuhp8;;d B. Where is the mass located when its potential energy is a maximum?

  Doubling only the amplitude of a vibrating mass-ah9(q w22szgae nd-spring system produces what effect on the system's mechanical swa(2 qez 29ghenergy?

  Doubling only the mass of a vibrating mass-and-spring system pro)b6ufk 2xvt x-duces what effect on the system's mechanical energk-62x t )bvxufy?

  Doubling only the spring cb 8n+cj,b*:zjj0jbl tonstant of a vibrating mass-and-spring system produces what effect on the system's mechanjcj+zj8t*n: bjb b, l0ical energy?

  A mass oscillates on the end of a sp ) 4plp.nz+5-j d3kqa yfu+pvtring, both on Earth and on the Moon. Where is the period the grpqn.5 tf+ak +p )- 4vzudjlpy3eatest?

  Increasing the spring constant k of a mass-and-spring sy hwixz4o oa+szr ,l(-fj42xt/stem causes what kind of change in the resonant frequency of the system? (Assume no change inlxhj,ar4iwx2 (o st+4zfz o/ - the system's mass m.)

  Increasing the mass M of a mass-and-spring system causes what kind of change 9mq 5nnl,b;1/ esn0 wmmkn/dsin the resonant frequency of the system? (Ass;m l /1n/,bms m9nkqnwes0dn5 ume no change in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spri*h05up4 hg m5esww2k;u 9+utzge 0mbxng system causes what kind of change in the resonant frequency of the system? (Am0u*p0s5u4tzg wehb x;29mku heg +5wssume 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 of len,mnmpxx n+7 90 xxfux8gth L. mump f x+8n7,xx90nxx For this system, when undergoing small oscillations

  When the mass of a simple pendulum is tripled, the time requi eg)0k(fxzr+ld3y1dc4vt/x 2m8yf +v kbw p2mred for one complete r bctf (xm2 3f81)lvxmpyw0 +ek ykzg+/dv4d2vibration

  Both pendulum A and B ad ff :i g6ifs-6.0xlzhre 3.0 m long. The period of A is T. Pendulum A is twice zli66s.i-ffhg f:0 xdas heavy as pendulum B. What is the period of B?

  When the length of a simple pendulum is tripled, ebz20+m6s qgzthe time for one complete vibration increaseezq26zg+sm0 b s by a factor of

  What happens to a simple pendulum's frequency if both its length and mgwby g 1-7dhy2ass are increased? y2hgyd 7-w1bg

  Simple pendulum A swings back and forth at twi k63e;grsqy/xxb5r *p ce the frequency of simple pendulum B. Which statement is corrqr6pb y3s /*r5xkg x;eect?

  If you take a given pendulum to the Moon, where the acceleration of gravihw0wi l0, t:*k j2olauty is less than on Earth, the res:kl oljuwa0,w* i2th 0onant frequency of the pendulum will

  Curve A in Fig. 11-1 represents 8.*ysjcs dad*

  Curve B in Fig. 11-1 hi)+xyrzm3bnh5w kp h/e4g 50.eaz7m represents

  Curve C in Fig. 11-1 rai(ga* qijd-oeeu nt0hg29jzd 17 (+1 zp )fjaepresents

  For a forced vibration, the amplitude of vibration is fouy9a.vec44kd b nd to depend on the

  In a wave, the maximum displacemenb7d/(1kiz ut5vn2vy jt of points of the wave from equilibrium is called the w/z(kn u5vi1vd2 yb7jtave's

  The distance between successive crests on a wn fxe t 15j+-f02 yqhidwxb,6kave is called the wave's

  The number of crests of a wave passing a point per unit time is cal,j(elb0 cych-5vqn:day y-+ bled the wave'sb0a-h- ,y ejq+nyc(l:bc5vyd

  For a wave, the frequency times the.,oarxn mp1 f19hu;o4lcy 8om wavelength is the wave's

  The frequency of a wav9 cjrkl4jmt /,e increases. What happens to the distance between successive crests if the speed remainsj k,rjt9l cm/4 constant?

  A wave moves on a string with wavelength l and frequency f. A sevxc kom4p5(y6cond wave on the same string has wavelength 2l and travels with the same velocity. What is the x5mcp(k6v yo4 frequency of the second wave?

  Consider a traveling wave on a string of length L, map*zk-ndo861w d*co fass M, and tension T. A standing wave is set up. Which of the fol zp1ood f8awn-dk*6* clowing is true?

  A string of mass m and length L 6+eaf+i u opssf-rs0fv*6 m4, cfm ol7is under tension T. The speed of a wave in the string is rsmfs*fm6,fav+i7 cu+ f-opsol 6e40v. 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 length?

  A string of mass m and length L is under tension T. The speed of a wave iecycbxo1 zkc* m+ oa ,.kk5;1on the string1cko xzc+;,ook*a e15 m. ybkc 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 is under tension ec:o)h mpu/ww4zt 5x5 T. The speed of a wave in the stwe5:uwc)o mtz/ph45x ring is v. What will be the speed of a wave in the string if the tension is increased to 2T?

  In seismology, the S *yk*hke1+yhu wave is a transverse wave. As an S wave travels through the Earth, the relue* hk1 y+k*hyative motion between the S wave and the particles is

  In seismology, the P wave is a longitudinal wave. As a P wave t*:t eo d1bwoj .k(f3wtravels through the Earth, the relativw1 b*e:o t jk3.w(otdfe motion between the P wave and the particles is

  The intensity of a wahrni-hp +/ *io2jrm.ky;tl o/ve is

  A wave pulse traveling to the right along utf9 plk73a)af -9 lwsa thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflecte fsawp9l laf)-u t379kd and transmitted pulses?

  Two wave pulses with equal positive amplitudes pass ead56pbeu;b * lcbo93drch other on a string, one is traveling toward the right and the other toward the left. At the point that they occupy t5ub eod;pb db3r6*9 lche same region of space at the same time

  Two wave pulses pass each other on a string. The one traveli*5qvt+9 z qtxohjl 2q;ng 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 5l+qvhtxq2;t*oq z9 jthat they occupy the same region of space at the same time

  Resonance in a system, such -:y) ia6edq9hz;zd hy 0 q+htbas a string fixed at both ends, occurs when

  If one doubles the tension in a violin string, t;akydqi 7.6w b yj9s7 0tphgl:he fundamental frequency of that stri 6agqty:y 09slwpd7j;bih7.k ng will increase by a factor of

  What is the spring constant of a spring that stretches 2.00 cm when a mass otq ayn.a*h*)ky6rfpk+g p 7g/f 0.600 kg is suspended f ygkkqh+g6 pfatr* .y*/7pn a)rom it?

  A mass is attached to a spring of spring constant 607v;2f,c3i1 ci pizef l N/m along a horizontal, frictionless surface. The spring is initially stretched by a force of 5.0 Nie32pl,f 7ii; fzvc1c 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 N/m along a horizontale+:rj;b gqiy/i9gk(8sln g 9lre, 4qu, 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 oscill eq,b9g g:rr +q94/ i; (ljuiensky8lgating. What is the period of oscillation?

  A mass is attached to a spring of spring constant 60 N/m along a hori,un ll;a1 t9f yfq+f:dzontal, 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 9 yf,qtudlfn:lf1; a+ when it is oscillating. What is the frequency of oscillation?

  A mass on a spring undergoes SHM. It goes through 10 completeu9sw b)warrj oog77-d8ge9g( oscillations in 5.07dw7gg r bgw(9ruej98) ooas- s. What is the period?

  A mass vibrates back and forth from the free end of an ideaj d6n pn)c( 9+t0rvzsr fa5uu1l spring of spring constant 20 N/m with an amplitude of 0.30 m. What is the kinetic energy of this vifv5s)u9 r1cru(t0 6 +p ndanjzbrating mass when it is 0.30 m from its equilibrium position?

  A 0.50-kg mass is attached to a spring of spring consta ,q3wuh cu/9dofx 1p-snt 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 of t3ocshf w-,x9/pu1u dq he system?

  A mass undergoes SHM with amplitude oc6ijq 4gdu,qvl2) ;: fktyv t3f 4 cm. The energy is 8.0 J at this time. The mass is cut in half, and the system is again set in motion with amplitude6u;tv2iqdkjgc 3yf q,)4vlt : 4.0 cm. What is the energy of the system now?

  A 0.50-kg mass is attached to a spring of spring constad8*zpv ( pvc*bnt 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and hasc z*p *vd(v8bp 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 ec qt09,2prmw along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of90p w rctqem,2 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 end of a horizontal spring of spring c yloq.jnm544 - 5ehkdtonstant 50 N/m and set into simple harmonic motion with an amplitude of 0.10 m.4ynljmh qd5 4oe .-5tk What is the total mechanical energy of this system?

  A 2.0-kg mass is attached to the end of a horizontal spring of spr vl. dc6h+7,;bxbnt hping constant 50 N/m and set into simple harmonic motion with an amplitude of 0.10 m. What is th7v b,h6h. tpc+blx ;dne total mechanical energy of this system?

  A mass vibrates back and forth from the free end of an ideal xeww5x7/c b ugq: 85hdspring of spring constant 20.0 N/m with a w5hgb8dx7:c qxeu5w/n 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 equ; tdf;27gr58fh3d uc (ju y4l3pjyxzyilibrium position and released. A frequency of 4.0 Hz is obser 4fy7ht3uyy;j3xg8zru;p cld2 (5 fjdved. 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 spring of spri1cn 9 6z k(6)t;nftnzn5phhd oq(c:mhng constant 10 N/m. The object is displaced b 6nhh615zq ncf(cotnn9(;tdkh: p)zmy
5.1 cm from the equilibrium position and let go. What is the period of vibration?

  A 4.0-kg object is attachedo 5(0w 46no ( ywn.svovf)yjqx to a spring of spring constant 10 N/m. The object is 6(4( 5vovwfnswo. j)0oxnq yy 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 from a spring of spring constant 18 N/m, displacef e-b:+ j/gs -lrkdc1qd slightly from its equilibrium position, and rele r/esc1kdlb-f +gj q:-ased. What is the frequency of its vibration?

  A mass is attached to a spring. It oscillates at a frequenj 3s1a+(a)oaxx 7e s0mnhoer0cy of 1.27 Hz when displaced a distance of 2.0 cm from equilib+jm1aa0sx oh3o a0 )xe7e(rsn rium and released. What is the maximum velocity attained by the mass?

  Two masses, A and B, are attached to different springs. Mass A w)b.6lmexkgrtnn58+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. Hoebn.)g5 n8 6lxr mtk+ww does the maximum speed of A compare to the maximum speed of B?

  A 0.30-kg mass is suspended on a spring. In equilrlrda8-.ck i,ibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm da,rki l .cr8-down and released from rest. Calculate the period of oscillation.

  A 0.30-kg mass is suspended on a spring. In equilibrium the ma697b feeqm*/ykp ch8v ss stretches the spring 2.0 cm dow6y/k7cb9v e 8pfehq m*nward. 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 suspended on a spri7r;wjm o 4l6dcng. In equilibrium the mass stretches the spring 2.0 cm downrj6 o ;74mdwclward. 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 versu8+duq zc-vp.j3dbb nog23 *mis time equatb dv3 8*2n jm.3-oubzqcgid+ pion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the following positht wi +zj 2s:hco5hhj2.ske+ . r3ekl3ion versus time equatioki .js.ch e3tj: l+ h52 +esho32zhkwrn:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple haged vn3nwi4ui9dw 11 zw (l; u4m..dqarmonic motion obeys the following position versus time equa4e9qd3 dud 1;l.zv nug 1aw4wim( .inwtion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes sim z6g.-4 luq; a i,zk.eu ib:pgyf5dy9yple harmonic motion accolu eg 6idibg ;qyukza 9.-5z,pyf4. :yrding 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 zf;phfvg9( j war/y(fc+ 8v-ey. f6)v zc;xgva force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the mass is released from re8fvezcg)+ch ;xf/ a fj- (vp(fv;y.z9g 6wvy rst 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.ljh,l fc)ltu8zn2c/3 t4bn+u (a) What are its frequency and period on Earhu c n)lt j3fn4,t2l c/ubl8z+th?

  A 3.00-kg pendulum is 28.84 m nk08su+ bayg6 l zpru u/:,7tslong. What is its period on Earth?

  A pendulum has a period of 0* 1eb2c2fe6v rckw ci2.0 s on Earth. What is its length?

  The pendulum of a grandfather clock is 1.0 m long. What is its period on;njih tozg4*8n ;3j md the Eartjt;ngih4zj m n*o3 ;8dh?

  The pendulum of a grandfather clock is 1.0 m long. What is its5bgl4 r1h,er5wrq 0c u *n3z8ilg z+nf period on the Moon where then5fb5c n,* 4 hlzrzeq r8gw1ugl 3i+0r 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 .b/ag3ji +fmcstring. 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 freqbmijc+. gaf3/uency would have resulted if a 0.50-kg mass (same diameter sphere) had been attached to the string instead?

A simple pendulum consistin,inuq1-zev ( vg of a 20-g mass has initial angular displacement of 8.0e. It oscillates with a per zvqi1v- e(nu,iod 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. / q7msjgwp-cav5h 48i The frequency of the wave is 120 Hz. What is the amplip7/m ci4 sah-8qwjg5 vtude?

  Figure 11-2 is a "snapshot" of a wave eo;5 qho ee1 h4bj9 cx 3i tt18u(vohbb2zh;8qat a given time. The frequency of the wave is 120 Hz. What is the waqe;he 93 c4q e21 o8xjuvi8hobz(b5tbto hh;1velength?

  Figure 11-2 is a "snapshot" of a wave at a given tzqk 1;s4 nyx4qime. The frequency of the wave is 120 Hz. Wha x1s44zkq nq;yt is the wave speed?

  What is the frequency of a wave whic9c vxzu f;l41yh has a period of 6.00 ms?

  What is the period of a wave with a frequ9j;w /a rqf;:yimcux6ency of 1500 Hz?

  What is the wave speed ifqrvc19/nv ph(itw1 vp4*mfa) a wave has a frequency of 12 Hz and a wavelength of 3.0 m)1(art vf im w1nvh/*9ppvcq 4?

  What is the velocity of a wave that has a wavelength of 3.0 q m 0mx)ob:o4so8 fsf5m and a frequency of 12 8sfxq)4osoo:fmbm0 5 Hz?

  What is the frequency of a 2.5 m wave traveling2fofuj5r/o. mvga; t ; at 1400 m/s?

  A piano string of linear mass density 0.00wy 9t4 i2k hn-5tl8rqr50 kg/m is under a tension of 1350 N. r52 4w yntkt9q8i-rhl What is the wave speed?

  A string of linear density 6.0 g/m is under a tension of 180 N. Whatd:66a g uvvqq3sm;1 jm is the velocity of pmu3 6;qvdg: a 16vjsmqropagation of transverse waves along the string?

A wave whose wavelength is 0.500 m is traveling down a 500 m long wire g lx 9 m8c+k-tv(g::zksjdk+v whose total mass jx c:(gmk-g vtvs+l9d 8:zk+kis
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 transqylc )7j7hjlx2fe,o3 verse wave on a 2.0-m long string fixed at both ends is 200 m/s. Which one of the following is not a resonant frequen lo, hfq7xjjy 3lec)72cy of this string?

  If a guitar string has a fundamental frequee /kzx xtx0u89c5yr2 bncy of 500 Hz, which one of the following xx x c9tkyez br280u/5frequencies can set the string into resonant vibration?

  A stretched string is observed to have four equal segments in a standing wav 5r (v8/xj q5jm./(tdl zyapxee driven at x8y.5 mp(tv/e(aj/ x zjql5d ra frequency of 480 Hz. What driving frequency will set up a standing wave with five equal segments?

  A string, fixed at both ends, woflslw*g:n6 2wf4r;vibrates at a frequency of 12 Hz with a standing transverse wave patternwg26o;fl :4rfns*wl w 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 tension of 20 N. What sh7k6*udvcme,k j1b r;nould its length be if its fundamental resonance frequency is 220 Hz?k,njvb 7 umkc16r* ;ed

  Find the first three harmonics of a string of linear mass density l(ilt4 e 6m qu0bdpw222.00 g/m and length 0.64depwq6l 0l( mti b22u00 m when it is subjected to tension of 50.0 N.

A string of length 2.5 m is fixed at both ends. W:1,l snj ni0g;5szsc4e/jbe phen the string vibrates at a frequency of 85 Hz, a standing wave with five loops :104 zelpjje/ibsns c5n g;,s 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.