Simple Harmonic Motion (SHM) Understanding

1. Envision holding the end of a ruler with one hand and deforming it with the other. When you let go, you can see the oscillations of the ruler. In what way could you modify this simple experiment to increase the rigidity of the system?

1. Describe a system in which elastic potential energy is stored.

1. It is weigh-in time for the local under-85-kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke's law and is depressed 0.75 cm by its maximum load of 120 kg. (a) What is the spring's effective spring constant? (b) A player stands on the scales and depresses it by 0.48 cm. Is he eligible to play on this under-85 kg team?

1. A tire has a tread pattern with a crevice every 2.00 cm. Each crevice makes a single vibration as the tire moves. What is the frequency of these vibrations if the car moves at 30.0 m/s?

1. A mass attached to a spring oscillates and completes 50 full cycles in 30 s. What is the time period and frequency of this system?

1. Identify an event in your life (such as receiving a paycheck) that occurs regularly. Identify both the period and frequency of this event.

1. Suppose you pluck a banjo string. You hear a single note that starts out loud and slowly quiets over time. Describe what happens to the sound waves in terms of period, frequency and amplitude as the sound decreases in volume.

1. A particle of mass 100 g undergoes a simple harmonic motion. The restoring force is provided by a spring with a spring constant of 40 Nm1. What is the period of oscillation?
   1. 10
   2. 0.5
   3. 0.1
   4. 1

1. Explain why you expect an object made of a stiff material to vibrate at a higher frequency than a similar object made of a spongy material.

1. A ball is attached to a string of length 4 m to make a pendulum. The pendulum is placed at a location that is away from the Earth's surface by twice the radius of the Earth. What is the acceleration due to gravity at that height and what is the period of the oscillations?

1. Pendulum clocks are made to run at the correct rate by adjusting the pendulum's length. Suppose you move from one city to another where the acceleration due to gravity is slightly greater, taking your pendulum clock with you, will you have to lengthen or shorten the pendulum to keep the correct time, other factors remaining constant? Explain your answer.

1. What is the period of a 1.00-m-long pendulum?

1. Why does it hurt more if your hand is snapped with a ruler than with a loose spring, even if the displacement of each system is equal?

1. You are observing a simple harmonic oscillator. Identify one way you could decrease the maximum velocity of the system.

1. A mass of 1 kg undergoes simple harmonic motion with amplitude of 1 m. If the period of the oscillation is 1 s, calculate the internal energy of the system.