Module 7—Oscillatory Motion

Lesson Summary

 

As you worked through this lesson, you should have developed an understanding of simple harmonic motion and now be able to answer these questions:

A pendulum demonstrates simple harmonic motion when the amplitude of the motion is small and the restoring force is proportional to the displacement of the pendulum relative to the equilibrium position. The displacement and force are always in opposite directions.

 

The restoring force of a pendulum is the component of gravity that acts along the arc to pull the mass back towards the equilibrium position. Mathematically, the relationship is expressed by

 

 

The period of a pendulum is the time required to complete one cycle. It is dependent on the length of the pendulum and acceleration due to gravity. Mathematically, the relationship is expressed by

 

 

The period for simple harmonic motion can be the same as that for circular motion. The radius of the circular motion is identical to the amplitude of the simple harmonic motion. This fact is observed in the conversion of the simple harmonic motion of a pendulum into the uniform circular motion of the hands on a clock.