Simple Harmonic Motion, Exercises of Physics

Download Simple Harmonic Motion and more Exercises Physics in PDF only on Docsity! University Physics (Prof. David Flory) Chapt_16 Thursday, November 15, 2007 Page 1 Name: Date: 1. A simple pendulum consists of a small ball tied to a string and set in oscillation. As the pendulum swings the tension force of the string is: A) constant B) a sinusoidal function of time C) the square of a sinusoidal function of time D) the reciprocal of a sinusoidal function of time E) none of the above 2. A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are: A) 40cm, 2 Hz B) 20cm, 4 Hz C) 40cm, 2 Hz D) 25cm, 4 Hz E) 20cm, 2 Hz 3. The table below gives the values of the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion. Which of these takes the longest time for its mechanical energy to decrease to one-fourth of its initial value? & b 1 A ko bg tg B 3h 2bp gl c kyf2 6p 2g D 4kg bg 2g Ep 10a A) A B) B Cc) Cc D) D E) E Write the letter for the correct answer on the answer sheet. Write clearly. University Physics (Prof. David Flory) Chapt_16 Thursday, November 15, 2007 Page 2 4. An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time: A) its amplitude is an increasing function of time B) its amplitude is a decreasing function of time C) its amplitude is constant D) its amplitude is a decreasing function of time only if the damping constant is large E) its amplitude increases over some portions of a cycle and decreases over other portions 5. The displacement of an object oscillating on a spring is given by x(t) = X cos (@t + @p). If the object is initially displaced in the negative x direction and given a negative initial velocity, then the phase constant @ is between: A) Oand 7/2 rad B) 2/2 and mrad C) a and3a/2 rad D) 32/2 and 27rad E) none of the above (@ is exactly 0, 7/2, , or 32/2 rad) 6. A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be: A) half the natural frequency of the oscillator B) the same as the natural frequency of the oscillator C) twice the natural frequency of the oscillator D) unrelated to the natural frequency of the oscillator E) determined from the maximum speed desired 7. It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different: A) masses B) periods C) amplitudes D) spring constants E) kinetic energies Write the letter for the correct answer on the answer sheet. Write clearly. University Physics (Prof. David Flory) Chapt_16 Thursday, November 15, 2007 Page 5 15. A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by 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: A) 0.13 m/s B) 0.18 m/s C) 3.7 m/s D) 5.2 m/s E) 13 m/s 16. In simple harmonic motion: A) the acceleration is greatest at the maximum displacement B) the velocity is greatest at the maximum displacement C) the period depends on the amplitude D) the acceleration is constant E) the acceleration is greatest at zero displacement 17. A particle is in simple harmonic motion along the x axis. The amplitude of the motion is X. At one point in its motion its kinetic energy is K = 5 J and its potential energy (measured with U =0 at x = 0) is U=3 J. When it is at x = X, the kinetic and potential energies are: A) K=5JandU=3) B) K=5JandU=-3J C) K=8JandU=0 D) K=OandU=8) E) K=OandU=-8J 18. In simple harmonic motion, the magnitude of the acceleration is: A) constant B) proportional to the displacement C) inversely proportional to the displacement D) greatest when the velocity is greatest E) never greater than g Write the letter for the correct answer on the answer sheet. Write clearly. 19. 20. 21. 22. University Physics (Prof. David Flory) Chapt_16 Thursday, November 15, 2007 Page 6 An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is vo and in the second it is 4vo. In the second trial: A) the amplitude is half as great and the maximum acceleration is twice as great B) the amplitude is twice as great and the maximum acceleration is half as great C) both the amplitude and the maximum acceleration are twice as great D) both the amplitude and the maximum acceleration are four times as great E) the amplitude is four times as great and the maximum acceleration is twice as great The amplitude and phase constant of an oscillator are determined by: A) the frequency B) the angular frequency C) the initial displacement alone D) the initial velocity alone E) both the initial displacement and velocity A 0.20-kg object attached to a spring whose spring constant is 500 N/m executes simple harmonic motion. If its maximum speed is 5.0 m/s, the amplitude of its oscillation is: A) 0.0020 m B) 0.10m C) 020m D) 25m E) 250m The amplitude of oscillation of a simple pendulum is increased from 1° to 4°. Its maximum acceleration changes by a factor of: A) 1/4 B) 1/2 © 2 D) 4 E) 16 Write the letter for the correct answer on the answer sheet. Write clearly. University Physics (Prof. David Flory) Chapt_16 Thursday, November 15, 2007 Page 7 23. A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g, and a is: 25. A) B) C) D) E) 2n Lig 2nJfLi(g+ a) 2nJLi(g-a) 2nJLla (W/2m)afg/L . A certain spring elongates 9.0 mm when it is suspended vertically and a block of mass M is hung on it. The natural angular frequency of this block-spring system: A) B) C) D) E) is 0.088 rad/s is 33 rad/s is 200 rad/s is 1140 rad/s cannot be computed unless the value of M is given An object attached to one end of a spring makes 20 vibrations in 10 s. Its frequency is: A) B) C) D) E) 2 Hz 10s 0.05 Hz 2s 0.50 s Write the letter for the correct answer on the answer sheet. Write clearly.