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Transcript

Homework Set 3: SHM Name: _______________________ 1. A mass moves back and forth in simple harmonic motion with amplitude A and period T. a) In terms of T, how long does it take for the mass to move through a total distance of 2A? b) How long does it takes for the mass to move through a total distance of 3A? 2. A positive versus time plot for an object undergoing simple harmonic motion is given below. Rank the six points indicated on the graph in order of increasing speed, velocity and acceleration. Indicate a tie where necessary. 3. An object moves with simple harmonic motion. If the period of the motion is doubled, by what factor do the following quantities change? a) angular frequency b) frequency c) maximum speed d) maximum acceleration e) total mechanical energy 4. A mass on a spring oscillates with simple harmonic motion of amplitude A about the equilibrium position x = 0. Its maximum speed is vmax and its maximum acceleration is amax. a) What is the speed of the mass at x = 0? b) What is the acceleration of the mass at x = 0? c) What is the speed of the mass at x = A? d) What is the acceleration of the mass at x = A? 5. A child rocks back and forth on a porch swing with an amplitude of 0.24 m and a period of 2.80 sec. Assuming the child’s motion is harmonic, find the child’s maximum speed. 6. A spring with a force constant of 65 N/m is attached to a 0.50 kg mass. Assuming that the amplitude of motion is 3.1 cm, determine the following: a) angular frequency b) maximum velocity c) period 7. A 0.321 kg mass is attached to a spring with a force constant of 12.3 N/m. If the mass is displaced 0.256 m from equilibrium and released, what is its speed when it is 0.128 m from equilibrium? 8. How would you answer to problem 7 change if the following changes were made to the initial system? a) The mass was doubled. b) The spring constant was increased by a factor of 4. c) The displacement was halved. 9. A simple pendulum of length 2.5 m makes 5 complete swings in 16 seconds. What is the acceleration due to gravity at the location of the pendulum? 10. A pendulum on Earth has a period of exactly 1 sec. a) What is the length of the pendulum? b) How would the pendulum have to be changed to keep a period of 1 second if it was moved to the Moon where gravity is 1/6th of the Earth’s? 11. What is the physical cause of resonance? What caused this in the case of the Tacoma Narrows Bridge? 12. What happens to each of the following in a dampened oscillation? a) Kinetic Energy b) Elastic Potential Energy c) Spring Constant d) Displacement of mass e) Temperature of the mass