SIMPLE HARMONIC MOTION
REVIEW SHEET
1. How is periodic motion related to simple harmonic motion?
2. If a pendulum clock loses time, should the pendulum be made shorter or longer? Explain.
3. Explain why less net force is exerted on the mass in the figure below as the mass returns to its
equilibrium position. Mark the points of minimum and maximum velocity, force and acceleration.
m
4. An airplane loops-the-loop in a vertical circle, picking up speed as it approaches the bottom of
the loop and losing speed as it approaches the top of the loop. How does the shadow of the
plane move across the ground relate to SHM? How does the radius of the reference circle relate
to amplitude of the swing for the shadow in SHM?
5. The velocity at the end points of a vibrating is zero, but the acceleration is a maximum. Give
another example (not SHM) where the acceleration of a body is not zero when the velocity is
zero.
6. You are asked to find the height of a room and, being without a tape measure but in possession
of a watch, you hand a string from the ceiling, put a weight on the other end, and adjust it so that
it just about touches the floor. Then you swing it as a pendulum and find that the period is 3.56
seconds. How high is the room?
7. Find the period of vibration of a mass on the end of a thin steel bar if a force of 25 N displaced
the bar by 0.015 m. The mass is 2.5 kg.
8. A spring scale that is used to find the mass of objects like fish has the distance between the 0
mark and the 10 kg mark is 5.0 cm. What is the spring constant in MKS units?
9. For a vibration of amplitude 0.l0 m to have a maximum acceleration of g, what would the period
have to be?
10. A child on a swing is in motion with a period of 4 s and an amplitude of 2.5 m. (a) Find the
maximum speed. (b) Find the maximum value of the acceleration. (c) At what points does the
maximum acceleration occur? (d) In what direction is the acceleration at the positions where it
is maximum? (e) If you were on the swing, at the points of maximum acceleration, what is the
direction of the force you would experience?
ANSWERS TO THE PROBLEMS:
6. 3.15 m
7. 0.24 s
8. 1960 N/m
9. 0.63 s
10. (a) 3.9 m/s (b) 6.17 m/s (c) at maximum displacement (d) toward the center (e) outward
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