The time for one cycle of a periodic process is called t)n yfbz ;jy w(729fpr 3vg0 a su6rywkc))ku:ehe

  For a periodic process, the num8c 5ofn uquy, z.pg-n2ber of cycles per unit time is called the

  For vibrational motion, the maximum displacement fromx/.u2d6oz maa the equilibrium point is called theadua xz6m2o /.

  A mass on a spring undergoes SHM. When the mass is at its maximumk aba6p +i.gzmcvk;:9 displacement from equilibrium, its insvpzmk+a:6 b;gai .k c9tantaneous velocity

  A mass on a spring undergoes SHM. Whenl+ldaal49, e 7x3imdw the mass passes through the equilibrium position, its instantaneous vw 34laim9 7 ald,l+xdeelocity

  A mass on a spring undergoes SHM. When the mass is at maximum displacement from(ixye5s8/ eekthd,* j xp4c;la4;y ny equilibrium, its instantaneous xsa dy4e,k ;typcnehi;e jl 84 *x/y(5acceleration

  A mass is attached to a vertical spring and bobs up and down between-8f)l uxge+8 qk26wggbsx sm4 points A and B. Where is the mass located when itsg+ -4qbelug6sg w2xx8 m) s8kf kinetic energy is a minimum?

  A mass is attached to a vertical spring and bobs u) : ryk0+or)u qta2jj)ayof:tp and down between points A and B. Where is the mass loc: +q))jur2oyk )j0:aao ryfttated when its kinetic energy is a maximum?

  A mass is attached to a vok jg.6urd*9rj v3pe)ertical spring and bobs up and down between points A and B. Where is the mass located when its potential energy is a mi9ru3g.je*krjo6dp) vnimum?

  A mass is attached to a vertical spring and bobs up and down between pointskgv(4edr .eo. A and B. Where(kr.eo g d.v4e is the mass located when its potential energy is a maximum?

  Doubling only the amplitude of a vibrating mass-and-spring saozjq82 l8p;dr(jq q:ystem produces what effect on the system's mechanicajld2:r opq8; az qq8(jl energy?

  Doubling only the mass of a vibrating mass-and-spring systemqfpun6eocj 8i,jr,+2vhya: . qo5c1m produces what effechm5qi2nr6eyj apc81qvc . foj ,,:u+ot on the system's mechanical energy?

  Doubling only the spring constant of a vibrating mass-and-spring system produk 5y5ys6x bpshpdf+3i+ /yd.hces what effecdhb+y/s 5ihx.ds5y3 ykp+fp6t on the system's mechanical energy?

  A mass oscillates on the end of a sr,83 7won9*z di0sha eh zu+bspring, both on Earth and on the Moon. Where is the period t*be,sdhhzs 8w+z3i97 r o0unahe greatest?

  Increasing the spring constant k of a mass-and-spri:hl9 1+opzttswk )u w;wo8 )xsng system causes what kind of change in the rz w)t+os8ktlo:p; )swwh xu 91esonant frequency of the system? (Assume no change in the system's mass m.)

  Increasing the mass M of a mass-and-sprinvj olis1hd :g.l0la2 tz w)whn(48 ;fzg system causes what kind of change in the r1z hw8j ;:g)a2t0lofnhsdiw. 4vl(z lesonant frequency of the system? (Assume no change in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spring system causy )*ng/3*ijs9 qnj tpces what kind of change in the resonant frequency of the sy/s 9pn qgjct)jin*y3*stem? (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 attached to a weightless string of l/.5n3 il o8ifujp8og length L. For this system, when undergoinno/5 l3i gouj8i l8f.pg small oscillations

  When the mass of a simp :o+uvr/w.7 da 5qmwjrle pendulum is tripled, the time required for one complete vibra w:5ra/v uqo7j+.mr wdtion

  Both pendulum A and B are 312abe- mpia/mt.m8siab t, w9*waed 3.0 m long. The period of A is T. Pendulum A is twice as heavy as pendulum B. What is the period of Bdws*3.i-m2b8tta w ap m9bemie ,a/1a?

  When the length of a simple pendulum is nt ;l cgm ey6mfr965w(,ot1zhtripled, the time for one complete vibration96lr1hwmfgoc(, 5tmte;n y z6 increases by a factor of

  What happens to a simple pendulum's frequency if both its length and mass ar j/w9aif0pdu 4jhw)u +e increas u)9dupjwh/j ia f4w0+ed?

  Simple pendulum A swings back and forthzuxh0(sy dx,ox;4 h- h at twice the frequency of simple pendulum B. Whi- xhuhh 4z ;xsyodx(0,ch statement is correct?

  If you take a given pendulum to the Moon, where the acceleration of gravityai.lyl feg:un1 mhdb)u2 4 h.. is less than 41i:e.a2bgy. n) huh.df mlluon Earth, the resonant frequency of the pendulum will

  Curve A in Fig. 11-1 repsr)6k0:l5v oacu k 8qzresents

  Curve B in Fig. 11-1 repreqb),24,a duv i -qsbzmsents

  Curve C in Fig. 11-1 b kyq8.nr8 fd5:kxy.s represents

  For a forced vibration, theq2 9 9rr8wpvvm fpt,v-ai- ;i5ew3z la amplitude of vibration is found to depend on the

  In a wave, the maximum displacement of points of the wave froc2nmpk2);i kb1g+o 0vuig*r p m equilibrium is called the wave'+;p0n)oci *1mibr2kgpg vuk2s

  The distance between successive crests o-:f.x 2b skslmn a wave is called the wave's

  The number of crests of a wave passing a pointht *hk) gb+r 7i;lh d w,59vika/fb+ip per unit time is called the wave's k ri5dabv ),t hwgh 7+*;kf/ih9bl+ip

  For a wave, the freqz:u3q8 bxgqeo *z;(l xuency times the wavelength is the wave's

  The frequency of a wave increases.1halq82 ,nb tc)i o4*adpmsh4 What happens to the distance between successive crests if the specnh tqsaim48a p,hdl 24b o1*)ed remains constant?

  A wave moves on a string with wavelength l and freqlg tlzh7;:ki 40m sy0duency f. A second wave on the same string has wavelength 2l00lmksdhg: t 7;zl4yi and travels with the same velocity. What is the frequency of the second wave?

  Consider a traveling wave on acqpz;ia d f-e,x/y2j) string of length L, mass M, and tension T. A standing wave is set up. Which o-;q/) iy fepjd,cazx2f the following is true?

  A string of mass m and length L is under tension T. The speed o3lp5 ms:u.pxk f a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is incrpl.:sk3 u5 mxpeased to 2m, with no change in length?

  A string of mass m and length L i ny n4r8bu r4xftmo *cc5du,)9b u-e7as under tension T. The speed of a wave in the string is v. What will be the speed ,t 8on rua-54 y9b c4*cu7funrbdex)mof 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 un+j1pyel 8o6vc; /w uclder tension T. The speed of a wave in the stl1+; vl8u jc6ope/y cwring is v. What will be the speed of a wave in the string if the tension is increased to 2T?

  In seismology, the S wave is a transverse wave. z)ja6yl e+6wczhti02 As an S wave travels through the Earth, the relative motion between the S wajw 2+66zaizl0yhte)cve and the particles is

  In seismology, the P wave is a longitudinal wave. As a P wdjncq:-enos zvc63p 9 ww5-d9ave travels through the Earth,v-q jo-9s9:e6d ccw5 wznpnd3 the relative motion between the P wave and the particles is

  The intensity of a waab )o1zr (yfqvhh/q+7ve is

  A wave pulse traveling to the right along a thin cord reaches a discontinuity3i )im)6dzn: *3/phoy4ii yflgxks.3 dj4rpv where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?f*/34g rni 3 yli6 pzx3mdjiosd:)y.vpi4)kh

  Two wave pulses with equal positive ampzh ,pd;vam*k9eu dewf) ps -g.lt)x:3ab dh)3litudes pass each other on a string, one is traveling toward the right and the other toward the left. At the point that they occupy the same region of space atf ;l:gb evds,3hu)h-m .3a kddpp9)e axt)w*z the same time

  Two wave pulses pass each other on a string,e st5u py64uq. 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 saq4ye,p5uus 6 tme region of space at the same time

  Resonance in a system, such as a string fixed ,;x:d4vf5my lo*z ipqat both ends, occurs when

  If one doubles the tension in a violin string,v*8fpk ps, vwuyjvkfe t5e+ssx/; +84 the fundamental frequency of that string will f syv pwxs kjv+8 ,keu*p+84v5e/st;fincrease by a factor of

  What is the spring constant of a spring th1; den px 6xy32wed-og1gwcq,at stretches 2.00 cm when a mass of 0.6x c y,dx6pgg-q e1o12d;wn w3e00 kg is suspended from it?

  A mass is attached to a spring of spryawz+-mkr ,n/ :f 86c4ukq bmking 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 let go. It takes the mass 0.50 s to go back to its equilibrium position when it is oscillating. What is m-6ub kacqrwy 8/z,k:k4 fn+mthe amplitude?

  A mass is attached to a spring of spring constant 60 N/m along a horiir cb-wha: 26azontal, frictiob-ira 2ah:w c6nless 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. What is the period of oscillation?

  A mass is attached to a spring of spring constant 60 N/m along a horizontal,a.owj85co7vop cv( p/5yqq 3nn tin56 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 whencw.tq7qoppn6va/vc3oinj5 5(yn 58o it is oscillating. What is the frequency of oscillation?

  A mass on a spring undergoes SHMwr1 czj(t3p +h. It goes through 10 complete oscillations in 5t1zp cr (jh3+w.0 s. What is the period?

  A mass vibrates back and forth from the frehq- *gjw01-2o lfvtnwe end 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 equilibriumwnl- ot0hq2gv j w-*f1 position?

  A 0.50-kg mass is att(c8 n m -ahcuqx3 i,siua1.9hkached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.h8.ai uxuhkmsaq-n 9cc,i( 315 m/s at the equilibrium position. What is the total energy of the system?

  A mass undergoes SHM with amplitude of 4 cm. The energy is 8* lro xra,t:0d.0 J at this time. The mass is cut in half, and the xld0t:,r*r aosystem 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 . mto5e35 ty57a;hg zi8 o5 zbxpxzo/aspring constant 20 N/m along a horizontal, frichzot5o oiex5y;zpx t5az7b38. /am 5gtionless surface. 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 20a:+l3i ti 5rdl N/m along a horizontal, frictionless +llt:i3 ia5rd 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 energy and the potential energy the same?

  A 2.0-kg mass is attached to the end of a horxe4*9bpcw5z:h 8 t yneizontal spring of spring constant 505 e9xc e :z*ytbh84npw N/m and set into simple harmonic motion with an amplitude of 0.10 m. What is the total mechanical energy of this system?

  A 2.0-kg mass is attached to the eb3.ra7f ksd -4zks1xo nd of a horizontal spring of spring constant 50 N/m and set into simple harmonic motion withk s4dka bo x.r1-s73zf 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 idyz/6v / li6xroygix+.eal spring of spring constant 20.0 N/m with an amplitude of 0.250 m. What is the maximum kinetic energy of this vibrating+yxgx y ior l6v6/./iz mass?

  The mass of a mass-and-spring system is displaced 10 cm from id+77 gyt8eecw65gzzf ts equilibrium position and rely5tc z+g 87fgeze76dweased. 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 a spring of spring cocx)6 ib8o a+vvnstant 10 N/m. The object isbc8)x+av io v6 displaced 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 oe7h r8,czn8 qh*/ v7bmv 04psigw-(oa2 djynspring of spring constant 10 N/m. The object is displace 78,nmaj-72*4r bh (oodcv hyp/8enq igzswv0d 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*n6g8 uu cmz+)x5sizg of spring constant 18 N/m, displaced slightly from its equilibrium position, and released. What is the frequency of its vibr +xg 5szz* ug8n6cmu)iation?

  A mass is attached to a sprin*xs /mb hiuf38g. It oscillates at a frequency of 1.27 Hz when displaced a distance of 2.0 cm from equilibrium and released. What is *s/mxuib h38f the maximum velocity attained by the mass?

  Two masses, A and B, are att)md (*q byo-3gdrun )nached to different springs. Mass A vibrates with amplitude of 8.0 cm (y* ddnguq o-bmr)n3) 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 suspez5q. x a2w rsy.k12rhtnded on a spring. 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 . 52rsk .hr1zxw2tyqa from rest. Calculate the period of oscillation.

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretchei82.tq2 tj 9n ve:iup-dyz a+.qm j6vas 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 total energy of iq-pe+2 j.d6ymavv8 n:tu jq9i.2 tz athe system.

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stretches z)) ibgbdmd4 ddo30)vv+ lwvgr:9t+s. * pncs the spring 2.0 cm downward. The mass is then pulled an add:+vs9z+ srg3 v4*) gdbobnvmwid .dd ctpl))0itional distance of 1.0 cm down and released from rest. Write down its equation of motion.

  An object in simple harmonic motion wiy(-(n w8nh) dzz8oosg0uw 9obeys the following position versus time equas)inz0- 8yw(dhgwwnu89 ozo (tion:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmmmros -n8i(k 3,+pj ixx6 w8cs+fl*fqonic motion obeys the following position versus time equation++,8*nmrxxi3 fkssc(loqjif8 -p6 w m:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys thk 0iq,w lhh74w u.t/hie following position versus time equatioiq7tw0i4hh/ ,h u.wlkn:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end of a spring executes simple harmonic motion accosv ngmhp,xfq4*fo9(w :ga97v rding to the equatiomvfxpf q9 oswhgn,97avg*(4:n $y = 0.50 \; \sin (18\pi \times t)$ where y is in meters and t is seconds. What is the period of vibration?

A 1.5-kg mass attached to sp:(v xuk.bb5gg5eb+ q hring with a force constant of 20.0 N/m oscillates on a horizontal, frictionless trac+:gb x 5g.5bveqkub (hk. 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. (a) What are its frequency at :wypjuc(94 and period on Eartpj utc:y(aw49h?

  A 3.00-kg pendulum is 28.84 m long. What is its period on5m 8fw+f)ekbvgaj- 4,inaz-u n2 , rxu Earth?

  A pendulum has a period of 2.0 s on Earthfgzn+ .3 vn*cv. What is its length?

  The pendulum of a grandfather clock is 1.0 m long6yvjkr am 4mr1nx+; c). What is its period on the Ear6; r) 4m najvc1y+kxmrth?

  The pendulum of a grandfather clockb4gw7fc8n4 mt is 1.0 m long. What is its period on the Moon where the acceleration due to gravitytgnb c8w4f74 m is only $1.7 \; m/s^2$?

  A simple pendulum consists ofiasc3 o vxq3113 /glzeu 9d(zo a 0.25-kg spherical mass attached to a massless 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-kgzl3z/ioxo se3vu9c(ad1q3 g1 mass (same diameter sphere) had been attached to the string instead?

A simple pendulum consisting of a 2077l 2*l 0bywhp7q vrvs-g mass has initial angular displacement of 8.0e. It oswv7 7ry hlbql 20pv7s*cillates 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. The frequency of gdm6bm-.f km/9jvz3 k the wave is 120 Hz. What is the ampkdvbjmm. z9 6-g/m3kflitude?

  Figure 11-2 is a "snapshot" of a wah9wy 5i:u;sabk9 iqu* ve at a given time. The frequency of the waveuyh uw9kaib* 9:; sqi5 is 120 Hz. What is the wavelength?

  Figure 11-2 is a "snapshot" of a wave at a given time. The frequenvz/gqtxk;.8h. jpnfo mr ld;cg*/y0 /cy of the wave isnglzmjd. r8q;gty/c v/xo h /.fp;k* 0 120 Hz. What is the wave speed?

  What is the frequency of a wave whz1 yf bao6*yqf i*v.(b ajr)8hich has a period of 6.00 ms?

  What is the period of a wave with a frequency of 1500 Hwa)qmyvuzr.q4q /24g z?

  What is the wave speed if a wave has a frequency of 12 Hz and a wavelengt q+f./qmx(oii3vvp kf h58 q1oh of 3.0 m?p.h+/qv ( imo3i8 xffoqqk1v5

  What is the velocity o3p(aker xy :/6 h4jgw4vyck, uf a wave that has a wavelength of 3.0 m and a frequency ofc,x4 :k4ve/ awp3uhyj6(kgr y 12 Hz?

  What is the frequency of ahssjwri: 55xb4:x 6 xy p0).whx4dfyc 2.5 m wave traveling at 1400 m/s?

  A piano string of linear mass density 0.0050 kg/mgcwzb8b 7 :oq3 is under a tension of 1350 N. What is the waveb 8boqw 3:zgc7 speed?

  A string of linear density 6.0 g/m is under a tension of 180 N. Wh : ip2l.ialqhrcvv . du)d/.kss;l-m) at is the velocity of propagation of transverse waves along vm ri)s : )ld;2.spuk-all/.idcq.hvthe string?

A wave whose wavelength is 0.500 m is traveling down ;yvndmc 0n0.dd z9/o qmt)y x5a 500 m long wire whose total ma5z;)ctn .9y dmov0y /m0qddnx ss 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 propaf(* s .6v:v ,6we5rk)sbk iojnhsw7bh gation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s. s f*iob6 5kwk.h6hsse rjv:,b 7vnw() Which 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 of theb3 3n5q xuyji4j2 o:qs following frequencies can set the string i2:q j5jiusbyo3 n4q3xnto resonant vibration?

  A stretched string is observedq(aocmx8 msu;e-mnq a 3fo,a5x21ky5 to have four equal segments in a standing wave driven at a frequemeq5uf akc8 xy-n1xm(5a mso3a; ,o2qncy 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 frequetndlf)5 fbw4 3ncy of 12 Hz with a standing transverse wave pattern containid f 5nb3wflt4)ng 3 loops. What frequency is needed if the standing wave pattern is to contain 4 loops?

  A string of linear density 1.5 g/ml*l*.8j rgkjvb ja-*+qhe0ja is under a tension of 20 N. What should its length be if its fundamental resonance f***hl ej8la q-jkv. jga0brj+requency is 220 Hz?

  Find the first three harmonics of a string of linear mass density 2.00 g/m f(f13 wo xtv.yl (pd2xand length 0.600 m when it is subjected to tension of 50.fw txyvdx(f31p2o (l.0 N.

A string of length 2.5 m is fixed at both 6xuz80 r3y dziends. When the string vibrates at a frequency of 85 Hz, a standing wave with five loo6i8z z3ru 0yxdps 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.