# Chapter 15 Homework Question 1 A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point.

Chapter 15 HomeworkQuestion 1A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. At which of thefollowing times is it furthest from the equilibrium point?0.7T0.5TT1.4T1.5TQuestion 2The acceleration of a body executing simple harmonic motion leads the velocity by what phase?0Pi/8 radPi/4 radPi/2 radPiradQuestion 3The displacement of an object oscillating on a spring is given by x(t) = xmcos( t + ). If the initialdisplacement is zero and the initial velocity is in the negative x direction, then the phase constant is:0Pi/2 radiansPi radians3Pi /2 radians2 Pi radiansQuestion 4The displacement of an object oscillating on a spring is given by x(t) = xmcos( t + ). If the object is initiallydisplaced in the negative x direction and given a negative initial velocity, then the phase constant is between:0 and Pi/2 radiansPi/2 and Pi radiansPi and 3 Pi/2 radians3 Pi/2 and 2 Pi radiansnone of the above ( is exactly 0, /2, , or 3 /2 radians)Question 5A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it. 200 rad/sis 1140 rad/scannot be computed unless the value of M is givenQuestion 6A 0.20-kg object mass attached to a spring whose spring constant is 500 N/m executes simple harmonic motion. Ifits maximum speed is 5.0 m/s, the amplitude of its oscillation is:Print Assignment: Chapter 15 Homework ::true http://edugen.wiley.com/edugen/shared/assignment/test/agprint.uni?numb…2 of 8 11/2/2010 2:15 PM0.0020 m0.10 m0.20 m25 m250 constant of 200 N/m. If the oscillation is startedby elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the maximum speed of the block is:0.13 m/s0.18 m/s3.7 m/s5.2 m/s13 m/sQuestion 8A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is startedby elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the amplitude of the oscillation is:0.13 m0.18 m3.7 m5.2 m13 mQuestion 9A block attached to a spring undergoes simple harmonic motion on a horizontal frictionless surface. Its total energyis 50 J. When the displacement is half the amplitude, the kinetic energy is:zero12.5 J25 J37.5 J50 JQuestion 10A mass-spring system is oscillating with amplitude A. The kinetic energy will equal the potential energy only whenthe displacement iszero± A/4± A/2± A/rad from 2anywhere between –A and +A*Question 11What is the maximum acceleration of a platform that oscillates with an amplitude of 2.8 cm at a frequency of 5.2Hz?Number________ *1 Units_________Significant digits are disabled; the tolerance is +/-2%*Question 12In Fig. 15-29, two identical springs of spring constant 160 N/m are attached to a block of mass 23 kg. The block isset oscillating on the frictionless floor. What is the frequency (in Hz) of oscillation?Number________ *1 Units__________*Question 13An oscillator consists of a block of mass 0.493 kg connected to a spring. When set into oscillation with amplitude 35cm, the oscillator repeats its motion every 0.439 s. Find the (a) period, (b) frequency (in Hz), (c) angularfrequency, (d) spring constant, (e) maximum speed, and (f) magnitude of the maximum force on the block fromthe spring.(a) Number________ *1 Units________(b) Number________ *2 Units________(c) Number________ *3 Units_________(d) Number________ *4 Units_________(e) Number_________ *5 Units________(f) Number *6 Units*Question 14An oscillator consists of a block attached to a spring (k = 372 N/m). At some time t, the position (measured fromthe system’s equilibrium location), velocity, and acceleration of the block are x = 0.101 m, v = -19.1 m/s, and a =-122 m/s2. Calculate (a) the frequency (in Hz) of oscillation, (b) the mass of the block, and (c) the amplitude of themotion.(a) Number________ *1 Units____________(b) Number________ *2 Units____________(c) Number________ *3 Units____________*Question 15When the displacement in SHM is equal to 1/7 of the amplitude xm, what fraction of the total energy is (a) kineticenergy and (b) potential energy? (c) At what displacement, in terms of the amplitude, is the energy of the systemhalf kinetic energy and half potential energy? (Give the ratio of the answer to the amplitude)(a)__________ *1(b)__________ *2(c)__________ *3*Question 16A block of mass M = 5.10 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring ofconstant k = 5780 N/m. A bullet of mass m = 8.50 g and velocity of magnitude 530 m/s strikes and isembedded in the block (Fig. 15-38). Assuming the compression of the spring is negligible until the bullet isembedded, determine the amplitude of the resulting simple harmonic motion.Number______________ *1 Units_______________Significant digits are disabled; the tolerance is +/-2%*Question 17If the phase angle for a block-spring system in ratio of the kinetic energy to the potential energy at time t = 0?Number *1 UnitsSignificant digits are disabled; the tolerance is +/-2%*Question 18A 81 kg solid sphere with a 15 cm radius is suspended by a vertical wire. A torque of 0.25 Nm is required to rotatethe sphere through an angle of 0.76 rad and then maintain that orientation. What is the period of the oscillationsthat result when the sphere is then released?Number_________ *1 Units_____________Significant digits are disabled; the tolerance is +/-2%*Question 19The pendulum in Fig. 15-40 consists of a uniform disk with radius r = 17.0 cm and mass 570 g attached to auniform rod with length L = 520 mm and mass 230 g. (a) Calculate the rotational inertia of the pendulum about thepivot point. (b) What is the distance between the pivot point and the center of mass of the pendulum? (c) Calculatethe period of oscillation.(a) Number________ *1 Units_________(b) Number________ *2 Units____________(c) Number________ *3 Units_________*Question 20Suppose that a simple pendulum consists of a small 70.0 g bob at the end of a cord of negligible mass. If the angleθ between the cord and the vertical is given byθ = (0.0781 rad) cos[(1.17 rad/s) t + φ],what are (a) the pendulum’s length and (b) its maximum kinetic energy?(a) Number______________ *1 Units__________(b) Number_______________ *2 Units___________*Question 21In Fig. 15-44, a stick of length L = 1.5 m oscillates as a physical pendulum. (a) What value of distance x betweenthe stick’s center of mass and its pivot point O gives the least period? (b) What is that least period?(a) Number________________ *1 Units__________(b) Number________________ *2 Units__________*Question 22A 1500 kg car carrying four 94 kg people travels over a “washboard” dirt road with corrugations 4.4 m apart. The carbounces with maximum amplitude when its speed is 19 km/h. When the car stops, and the people get out, by howmuch does the car body rise on its suspension?Number __________ *1 Units______________

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