The time for one cycle of a periodic process is wy sf9mq3; wk6.ymyh9);rqzecalled the

  For a periodic process, the n5 w+czum* 6* as8ybfkjycf*u-umber of cycles per unit time is called the

  For vibrational motion, the maximumevk/tee)pmd(13 fkm(dp7h ; e displacement from the equilibrium point is called;7(pvm3f(/e)mh kde e1 detkp the

  A mass on a spring undergoes SHlshr9 2hm hzgliv1): (M. When the mass is at its maximum displacement from equilibrium, its instantaneous veh9 1()mll2 hv gri:hzslocity

  A mass on a spring undergoes SHM. When the yg,o9.p5l cyymass passes through the equilibrium position, icgyo95,.pyyl ts instantaneous velocity

  A mass on a spring unw5 orh5b-rt-mdergoes SHM. When the mass is at maximum displacement from equilibrium, its instantan5 w-brr5thmo -eous acceleration

  A mass is attached to a vertica ng--w4o(ph2e0xav +v:y ynetl spring and bobs up and down between points A and B. Where is the mass located when its-t(g -+: ypnyex hva 24neovw0 kinetic energy is a minimum?

  A mass is attached to a vertical spring and bobs up and so))2 z hcff0 k1 ,0aamsg*ehau ;t-kqdown between points A and B. Where is the mazeha 1hk0s -;us )k) c,a ogf02fmt*qass located when its kinetic energy is a maximum?

  A mass is attached to x7 7(tudyzr +;c,eqyu a vertical spring and bobs up and down between points A and B. Where is the mass located when its potential energe; yd(u qyr,7+txu zc7y is a minimum?

  A mass is attached to a vertical spring and bobs up and down between;8nn c,3jip km points A and B. Where is thenc;n, 8jkm3 pi mass located when its potential energy is a maximum?

  Doubling only the amplitude of a vibrating mass-and-spring system produces wh28u3v6j dxb6,fr.kot myht u,at effect on thevj 2df 6bu8h 3yo,xur,6 ttm.k system's mechanical energy?

  Doubling only the mass of a vibrating mass-and-spring system produces what efij;z8sxbp )ttc8qdk n-.d6 y58l, jnefect on the system.lyc -nkbqpzx t8i 8nj,dj;s6)d e 8t5's mechanical energy?

  Doubling only the spring constant of a vibrating mass-an 2b4a7vcgdz 7xd-spring system produces what effect on the system's mechanical endx c7b zavg742ergy?

  A mass oscillates on the end of a spring, both on Earea.,8+c(c dde /hp rft7tzpm6th and on the Moon. Where is the period . p /ze+8m6 drcftpd,( 7etachthe greatest?

  Increasing the spring constant k of a mass-a2rry-ogsb .l,eens xf n4r)4 -nd-spring system causes what kind of change in the resonant freq2lo . xye4es )r-,-brrn4s nfguency of the system? (Assume no change in the system's mass m.)

  Increasing the mass M of a mass-and-spring system causes what kind of1;hr y;-fvja; vgns3px1; xqh change in the resonant frequency of the sy x-y3;pvhjrx v1; h;g 1snq;fastem? (Assume no change in the system's spring constant k.)

  Increasing the amplitude of a mass-and-spring system causes what kind of cha1+f,m vl ;zsalze.fgu2:q m:cnge in the resonant frequency of t afz:u;mlvz cs1.f,elmq:g2+ he system? (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 attachew*-q1gd r kn2p )dljn39l*as pd to a weightless string of length L. For this system, when undergoing lgq* w n-s3)dnjpdl*92 kpa1rsmall oscillations

  When the mass of a simple pendulum is tripled, the time required for or7e( x(c2n9nr guwwg0ne complet7gu2 9wwrc0((e nrn gxe vibration

  Both pendulum A and B are 3.0 m long. The period of A is T. Peqfe5 )h83qjr0:fbqmy1xd bb+8 ak , ez.ldf*rndulum A is twice as heavy as pendu)8df,hm 3y*rbbfekl 1fqbq :j +ex0q ad8z.5r lum B. What is the period of B?

  When the length of a simple pendulum is t+sz,ul-1l 9; pac 9enqqx-plcr 1n)n ebj9x+jripled, the time for one complete vibral p99u,-pn1j+nx;cq l)c nz e9eqsal +1rxj- btion increases by a factor of

  What happens to a simple pendulum's frequency if both iu6v(jje 0u92p xpo .cmts length and mass are increaseu.92pov6pc uj 0 j(mxed?

  Simple pendulum A swings back and forth at twice the frequency of simplhcu2 ; u bf 13ile2-xnyec.qw1e pendulum B. Which sy1un1ehexu22b . il wfc-c; q3tatement is correct?

  If you take a given pendulum to the Moon, wherem e t:ck8(qd0t the acceleration of gravity is less than on Earth, the resonant frequency ofe8ttk(m dq0c: the pendulum will

  Curve A in Fig. 11-1 reptnzcl338+ 3zm u(kzu;iag)q kresents

  Curve B in Fig. 11-1 repres ap( -2pemjd:xents

  Curve C in Fig. 11-1 represdb*+6ij;xqs lf,r m43c4gqnh ents

  For a forced vibration, th jtfnqqqzu6w2 b /mp1c4c; hvb :x)/h3e amplitude of vibration is found to depend on the

  In a wave, the maximum displacementyne g1+nfw :4b of points of the wave from equilibrium is called thy4engb:f1 nw+ e wave's

  The distance between successive crests )+5wx8:fuhp lig;ai aon a wave is called the wave's

  The number of crests of a wave passing a point per unit time is called the wave t+a;ys)uhn,: xdxac0 'xty:xu + a,a ds);cn0hs

  For a wave, the frequency times the wavelength is thex/nnl- vvqn u. n4e3u9 wave's

  The frequency of a wave increaw t8lilte( +/eses. What happens to the distance between successive crests if the speed remains constane wle+8it/lt( t?

  A wave moves on a string with wavelength l and frequen n-l;xed) w*w py0)njhcy f. A second wave on the same string has wavelength 2l and travels withwne;wx0n)ph l* jd) -y the same velocity. What is the frequency of the second wave?

  Consider a traveling wave on aj(ja f32 soa,rv9oj hf -6g/va string of length L, mass M, and tension T. A standing wave is set u vvo,-rf3a2osjj/6 af9(jha gp. Which of the following is true?

  A string of mass m and length L is under tension T. The speejb2hpk7zai0yy h j9 :4d of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string ihpz h9y4y70bkj ji2a :s increased to 2m, with no change in length?

  A string of mass m and length L is under tension T. The s( e(*ge ont/tp t* 7zcfy dog;3sv/.ippeed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L, wit7ge(i*tg.p*o enpct 3/z /vs;(oyf dth no change in mass?

  A string of mass m and length L is under tension T. The speed of a wave in the9 h;tambm-n s em9l1-m string is v. Whas-hle n9;1 tm9abm-mmt will be the speed of a wave in the string if the tension is increased to 2T?

  In seismology, the S wavein8vj/ zk ,-epsx+6tp is a transverse wave. As an S wave travels through the Earth, the relative motion between the S wave and the particj,8/ 6e nk+-ztpsvipxles is

  In seismology, the P wave is a longitudinal wave. As s8c),lxvi blj0 yjd): a P wave travels through the Earth, i,bd:) lcly)j80j xsvthe relative motion between the P wave and the particles is

  The intensity of a wave 6l b(4m2,hwtn m8fzze is

  A wave pulse traveling to the right along a thin n nc:lc y)a *33 hk4+m/rrrej(wjga7 hcord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and ga /7ca:wjh+hk)( *y3lenrcjn4mr r3 transmitted pulses?

  Two wave pulses with b e16lok+c/p2 xl (logequal positive amplitudes pass each other on a string, one is traveling toward the right and the other toward the left. At the pxl+gp1b /(e k26oolcl oint 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 ukv(8j8j +y: ww5tmgqright 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 sam k yujvq+8(:5tmww8gje region of space at the same time

  Resonance in a system, such as a qs2d2,hs ;nut string fixed at both ends, occurs when

  If one doubles the tension in a violin sfm0;3-u.ya7 het evgh ,v ;tnmtring, the fundamental frequency of that string will increase by a u ;0;g, .emv-vfe7hh3ayttnmfactor of

  What is the spring constant of a spring that stret t-3j vng,.fj 9ygr;alches 2.00 cm when a mass of 0.600rjv,g lt3a g-;jfy9n. kg is suspended from it?

  A mass is attached to a sprin j e3z ps:prqcr;6p+8ag of spring constant 60 N/m along a horizontal, frictionless surface. The spring is initially stretched by a force of 5.pr83z+s;p: aq6 rc pej0 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 tjn,y, fie;ae 0o a spring 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 let go. It takes the mass 0.50 s to go;nfje,0y iea, back to its equilibrium position when it is oscillating. What is the period of oscillation?

  A mass is attached to a jfzlnh;y/:a ,pr9tc h+m*g w7spring 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 let go. It takes the mass 0.50 szw tal*, rpcn+/g;yhh9 7mf: j to go back to its equilibrium position when it is oscillating. What is the frequency of oscillation?

  A mass on a spring undergoes9imd8 cj.cz;awv :52u4h rsec SHM. It goes through 10 complete oscillations in 5.0 s. What is thr. iuc avj ecm:z2sw89h4;5cde period?

  A mass vibrates back and forth from the free end of an ide) czyr 6 n,cx)vr0o2dpal spring of spring constant 20 N/m with an amplitude of 0.30 m. vd)ryr206czc)po,x n What is the kinetic energy of this vibrating mass when it is 0.30 m from its equilibrium position?

  A 0.50-kg mass is attachen0ab53 in or)jd to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed3jan 0bno)5 ri of 1.5 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 8.0o0qtt .u3r7k:o+ r h1 :twpzdvj k7o.c J at this time. The po.uk1 .q7dhoc3okwr0j: tt r vz:+t 7mass is cut in half, and the 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 t:);3sb)3bny 1 aui8 kykj ql1d2yujwzo a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object osq1sb) z 2nujw3k 1d3:ik a8blj;uy)yycillates 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 sfgjy0k 5-wvuf7 pf 8(xpring 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. At whaf jpu0x-5y(fvw7 fg 8kt location are the kinetic energy and the potential energy the same?

  A 2.0-kg mass is attached to the end+m ke9 tz+ m ekmhqsqxz6)wm94*:rp3 muc,1nl 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 of this syst*k9t1kqn hcsw3xmr emqm e+ 6l,+9)mu4 :pz mzem?

  A 2.0-kg mass is attached to the end of a horizontal spring of spring congha4k5qh j,;l stant 50 N/m and set into simple hj l4,a5h;kqgh armonic motion with an amplitude of 0.10 m. What is the total mechanical energy of this system?

  A mass vibrates back and forth fro315ac bd ad(pqm the free end of an ideal spring of spring constant 20.0 N/m with an amplitude of 0.250 m. What is the maxim1acqdba3 5(d pum kinetic energy of this vibrating mass?

  The mass of a mass-and-spring system is displaced 10 cm from its equilibriq92q0 fski hcurgld(1+g3; rium position and released. A frequency of 4.0 Hz is observed. What frequency would be observed if the mass had been displaced only 5.l9+ k qhrug1if srgi0q(c32;d0 cm and then released?

  A 4.0-kg object is attached to a spring of spring constant c52m8wx:hyv:-j-v dhuft y 0r 10 N/m. The object is displ5wjyx v:rhv-t 8u2yc0f-mdh :aced 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 springzb+b5hw l,kxusfe*2k : w7vo; constant 10 N/m. The object is displaced2w kzxk* ;fob,+w7ev lsub5h: 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 dn.) / tds)ylrwphso,/-hxz,constant 18 N/m, displaced slightly from its e)l)h/ n y ho/ dspzrtd,-ws,x.quilibrium position, and released. What is the frequency of its vibration?

  A mass is attached to a spring. It oscillates atzxaic fa z55f2f,gr *7pm, 22vpdhqy; a frequency of 1.27 Hz when displaced a distance of 2.0 cm from equilhpa*yd,v;z fmr p i725fxc25agfz 2 ,qibrium and released. What is the maximum velocity attained by the mass?

  Two masses, A and B, are attached to different springs. Mass A vibrates wit do g5 nhq2gtl9u04oky (j,/omh 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 speeo 0ok5d2,u4h lo/m( gytqjn 9gd of A compare to the maximum speed of B?

  A 0.30-kg mass is suspended on a spring. In equilibrium the mass stret41u z i8q/bjp6u gd4knches the spring 2.0 cm downward. The mass is then pulled an additional inq8d6z4bkjupu4/ 1gdistance 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 equilibrium the mass str:v :z n9wqoo. 5ud+vwletches 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 the systevzdquw:vl9.+ :5on wo m.

  A 0.30-kg mass is suspended on a spring. In equilias+08aj q v leu8r2b)k4+mdut brium the mass stretches the spring 2.0 cm dowbl u2km8s+r d0e8t jqua)v+4 anward. 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 timjao1;-vbz p)8hoew( -tw,nw2x g7kyie equw7po2(;j,tg h oi )eb1-awxz-yvkn8wation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the amplitude of vibration?

  An object in simple harmonic motion obeys the following position versus time eqk+lx,jr(mhvqn qd4. 9ukr4j ,(x mqd. +lqvn9hation:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the period of vibration?

  An object in simple harmonic motion obeys the following position versus 19m t4y3atj6 :.qkelhon wy1gtime equationo h:m w 9.gkl3te6yjq1 ytan41:
$y = 0.50 \; \sin (\pi/2 \times t)$. What is the maximum speed of the object?

  A mass attached to the free end o+37lc va 9behg5-s miaf a spring executes simple harmonic motion according to the eqea9ls7-ca +ghm3i vb5uation $y = 0.50 \; \sin (18\pi \times t)$ 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/o eure ryki1-pt+ .,g)m oscillates on a horizontal, frictionless track. At t= 0, the mass is releas+.-otp) e kygi1r,rueed 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 w3vh4 kx0d8- 3lbd ,ue+q lkewp*sx)uswings in 8.0 s. (a) What are its frequency and period on 0w-sd3q,x 8l+uh pu*elxd ) ewkv4k3bEarth?

  A 3.00-kg pendulum is 28.84 m long. wbmtv gme fctv(zjljd/*um9 o(7 ,ip;h4m:53 What is its period on Earth?

  A pendulum has a period of 2.0 s on Earth. n6-zfhpqx2l:e co97 e What is its length?

  The pendulum of a grandfather clock is 1.0 m long. What is its p0gj t1d)j rtt3eriod on the Earthgdtr1j0 tt3)j ?

  The pendulum of a grandfathil n 94bp)k7bher clock is 1.0 m long. What is its period on the Moon where the acceleratiobhl)7 i4b npk9n due to gravity is only $1.7 \; m/s^2$?

  A simple pendulum consists of a 0.25-w6cnqz fps3 ,+zr686kchv(smkg spherical mass attached to a massless string. ,ck zpmqs z+6n 6fcsw86r3h(v 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 diameter sphere) had been attached to the string instead?

A simple pendulum consisting eo nurwg yn4 )qbhr, 85.cf21nof a 20-g mass has initial angular displacement of n5y q f2hw.b41c 8rg)nnuore, 8.0e. It 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 "snapsh:fg+hrhbbb9fez+2t7jfe 5 +lx4 ) fh7gukz m8 ot" of a wave at a given time. The frequency of the wave izrg tjufh+b +k+gmfhf 2f79lbxb78) hz:54 ees 120 Hz. What is the amplitude?

  Figure 11-2 is a "snapsh* rvs 2isovy(2zt5v u:f )/4fw 0wgornot" of a wave at a given time. The frequency of the wave iso gi/4 z)*y vn5r0 22(:tsrovwfw fvsu 120 Hz. What is the wavelength?

  Figure 11-2 is a "snapshot" of a wave at a given times3ycavb3(i1osdo/* f)x* ribl w(7 zu. The frequency of the wave is( (bu 3rzd s/f1o l*wisi7)xaocv*by3 120 Hz. What is the wave speed?

  What is the frequency of a wave which has/qugv8n(1; n ub; z,6by5wznrlab u+s a period of 6.00 ms?

  What is the period ofk4l ,r wq)p/*io 1efut)m sjs4 a wave with a frequency of 1500 Hz?

  What is the wave speed if a wave has a frequency of 12 Hz ftq(j( xvv 2:cvb9g6rand a wavelength of 3. :(qc 9vt rvbfx(2jg6v0 m?

  What is the velocity of a wave that has a w 3ggm yh:k4,afz 6msy+avelength of 3.0 m and a frequency of 13mah+4g 6y,m:sy zkg f2 Hz?

  What is the frequency of a 2.5 m wave traveling at 1400 m/sytg14-- v8u77 w,dqkat mvg up?

  A piano string of linear mass density 0.0050 kg/m is und gl2a uf:ct.nzat-)aqf +/sx:16azc3(qd ncr er a tension of 1350 N. What is the waun:gt:x(+ n/.s1dc q3 a)facza6 qa2-rlz ftcve speed?

  A string of linear density 6.0 g/m is under a zx*d jlpt 3t9( v8 kj3ohj0my-tension of 180 N. What is the velocity of propagation of transvers y(jk9z3td joj8lmt*x-30v hpe waves along the string?

A wave whose wavelength is 0.500 m is traveling down a 500 m long wire whose totxxse cw20p f38al xpw80x e3 fsc2mass 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-m long string fixed , a9ij*kfp 13czv. fveat both ends is 200 m/s. Which one of the following is no ,f9e*. 1ivza3pc jvfkt a resonant frequency of this string?

  If a guitar string has a fundamental frequency of 500 Hz, which one of q-b x74yzzj4e the following frequencies can set the stringjqx4zby-z e 47 into resonant vibration?

  A stretched string is observed ku7xyug.m*:bto have four equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency: *muu7by xg.k will set up a standing wave with five equal segments?

  A string, fixed at both ends, vibrates at a frequency ofs58 arw2w x1 of6lj3dhpt)og2 12 Hz with a standing trax6so5jwpld a 8t 2h 32wrog)1fnsverse 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/m n 90 epqtke(0tsjvgk6 /.- wuvis under a tension of 20 N. What should its length be if its funda k 0vtn0ee vps6/t jg-k(9u.wqmental resonance frequency is 220 Hz?

  Find the first three harmonic aac cdbi8,:(ms of a string of linear mass density 2.00 g/m and lengthmcc(,:b8iada 0.600 m when it is subjected to tension of 50.0 N.

A string of length 2.5 m is fixed at bot wz*a- tazz e6(dfwg16h ends. When the string vibrates at a frequency of 85 Hz, a standing wave with five loops iwz a(aw1-dg 6e*f z6tzs 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.