Conceptual Questions:
1.
A simple pendulum is carried into an elevator. How does the period change,
if at all, when
a) the elevator accelerates upward,
b) the elevator moves at constant velocity, and
c) it decelerates upward?
2. In one of the problems below, the "energy of vibration" is given. Why is this energy a useful quantity for describing simple harmonic motion? What makes up this energy?
3. The kinetic energy of the bob on a simple pendulum swinging in simple harmonic motion has its maximum value when the displacement is at what point in its swing?
a. At zero displacement.
b. At 1/4 the amplitude.
c. At 1/2 the amplitude.
d. At the amplitude.
4. Which one of the following quantities is at a maximum when an object in simple harmonic motion is at its maximum displacement?
a. velocity
b. acceleration
c. kinetic energy
d. frequency
5. For a mass suspended on a spring in the vertical direction, the time for one complete oscillation will depend on:
a. the value for g (the acceleration due to gravity).
b. the distance the mass was originally pulled down.
c. the maximum speed of the oscillating mass.
d. the time doesn't depend on any of the above.
Numerical Problems: answers link to a help page.
1. A 0.2 kg object, suspended from a spring with a spring constant of k = 10 N/m, is moving in simple harmonic motion and has an amplitude of 0.08 m. What is its velocity at the instant when its displacement is 0.04 m? Hint: Use conservation of energy.
2. If one could transport a simple pendulum of constant length from the Earth's surface to the Moon, where the acceleration due to gravity is one-sixth (1/6th) that on the Earth, by what factor would the pendulum frequency be changed?
3. By what factor should the length of a simple pendulum be changed if the period of vibration were to be tripled?
4. A mass of 0.4 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the acceleration of the mass when at its maximum displacement of 0.1 m?
5. The oxygen molecule (02) may be regarded as two masses connected by a spring. In vibrational motion, each oxygen atom alternately approaches, then moves away from the center of mass of the system. If each oxygen in the molecule (mass m = 2.67 x10-26 kg) has a vibrational energy of 1.6 x10-21 J and the effective spring constant is 50 N/m, then what is the amplitude of oscillation of each oxygen atom?
6. An object moving in simple harmonic motion has an amplitude of 0.02 m and a maximum acceleration of 40 m/s2. What is the frequency of the system?
7. A simple pendulum of length 1 m has a mass of 100 grams attached, and is drawn back 30° and then released. What is the maximum velocity of the mass?
8. The motion of a piston in an automobile engine is nearly simple harmonic. If the 1 kg piston travels back and forth over a total distance of 10 cm, what is its maximum velocity when the engine is running at 3000 rpm?