Phy 231 Sp 03 Homework 13 Page 1 of 4 13 1A A particle will undergo simple harmonic motion if the restoring force acting on the particle is proportional to a The square root of the amplitude of motion of the particle b The frequency of oscillation of the particle c The particle s velocity d The particle s displacement from equilibrium e The square of the particle s displacement from equilibrium 13 2A Which one of the following is WRONG a A Hooke s law force will give simple harmonic motion b The frequency of oscillation is inversely proportional to the period of oscillation c For a given mass and Hooke s law spring the larger the amplitude of oscillation the larger the maximum speed d If you double the amplitude of oscillation of a mass on a Hooke s law spring you double its maximum kinetic energy e The potential energy of a mass on a Hooke s law spring is proportional to the square of its displacement from equilibrium 13 3A A 5 kg mass is hung on the end of a Hooke s law spring with force constant k 500 N m If the maximum speed of the mass is 5 m s what is its maximum displacement a 5 m b 50 m c 0 5 m d 0 05 m e You don t have enough information to tell 13 4A The maximum speed of a harmonic oscillator is 6 28 m s and its period is T 2 s What is its maximum amplitude of motion a 12 6 m b 0 5 m c 2 m d 3 14 m e You don t have enough information to tell 13 5A If the mass m at the end of a spring is replaced by a mass 9m the ratio fn fo of the new to old frequency of oscillation of the vibrating spring should be about a 1 9 b 1 3 c 3 d 9 e None of these is close 13 6A An object undergoing simple harmonic motion takes 1 sec to travel from one end point of its motion to the opposite end point What is the frequency of motion of this object a 2 Hz b Hz c 2 Hz d 2 Hz e 1 2 Hz 13 7A When a mass m 36 gm is hung on the end of an unstretched vertical massless spring the spring stretches by 0 4 m If the spring is then compressed by 0 1 m from this latter position about what should be the amplitude A and period T of oscillation a A 0 9 m T 1 3 s b A 0 9 m T 6 s c A 0 1 m T 6 s d A 0 1 m T 1 3 s e None of these is correct 13 8A Which one of the following statements is WRONG a The acceleration of a particle undergoing simple harmonic oscillation also varies simple harmonically b The total energy of a particle undergoing simple harmonic motion is constant c As a particle undergoes simple harmonic motion its energy oscillates between all potential energy at one limit and all kinetic energy at the other limit d If the tension in a string is constant the speed of a wave on the string should not change when the wavelength doubles e If the tension in a string is constant the frequency of oscillation should double when the wavelength doubles 13 9A A pendulum of length L undergoes simple harmonic motion at the earth s surface due to the gravitational force mg Which one of the following is the correct expression for the angular frequency of the pendulum a g L b L g c L g d g L e gL 13 10A A pendulum of a certain length has a period of 2 s If you reduce the pendulum s length to 1 4 of its initial value what is the new period a 1 s b 2 s c 0 5 s d 8 s e 4 s 13 11A The distance between the crest and neighboring trough of a sinusoidal water wave is 3 m If the frequency of this wave is 2 Hz what is the speed of the wave a 1 5 m s b 12 m s c 6 0 m s d 3 m s e You don t have enough information to tell 13 12A If you double the tension in a string and simultaneously double its mass per unit length the ratio of new to old wave speed is a 1 2 b 2 c 1 d e 4 Phy 231 Sp 03 Homework 13 Page 2 of 4 The location x as a function of time t of a particle undergoing Simple Harmonic Oscillation is given by x Acos t Acos 2 ft 13 13A If f 1 Hz what is the particle s location at t 0 25 sec a 0 b A c A 2 d A e 0 87A 13 14A If 1 rad sec what is the particle s location at t 2 sec a 0 b 0 87A c A 2 d A e A 13 15A Which one of the following statements is WRONG a If a pendulum clock is running slow you could speed it up by shortening the length of its pendulum a bit b If a pendulum clock is running slow you could speed it up by shaving a bit of material off of the mass at its end c You could increase the wave speed in a rubberized string by pulling harder on the string to increase its tension d You could increase the wave speed in a rubberized string by decreasing the mass per unit length of the string e A pulse that reflects from a fixed end of a string moves back with displacement opposite to that it had coming in Phy 231 Sp 03 Homework 13 Page 3 of 4 13 1B A particle will undergo simple harmonic motion if the potential energy of the particle is proportional to a The square of the amplitude of motion of the particle b The frequency of oscillation of the particle c The particle s velocity d The particle s displacement from equilibrium e The square of the particle s displacement from equilibrium 13 2B Which one of the following is WRONG a A Hooke s law force will give simple harmonic motion b The frequency of oscillation is proportional to the period of oscillation c For a given mass and Hooke s law spring the larger the amplitude of oscillation the larger the maximum speed d If you double the amplitude of oscillation of a mass on a Hooke s law spring you quadruple its maximum kinetic energy e The potential energy of a mass on a Hooke s law spring is proportional to the square of its displacement from equilibrium 13 3B A mass m 4 0 kg hanging from a spring with force constant k 80 N m is set into vertical motion starting from rest with initial displacement …
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