Simple Harmonic Motion

If moving objects repeat their path over a regular interval, it is called harmonic or periodic motion. Periodic motion in which an object moves to and fro from a fixed point is called oscillation.

If the restoring force on the object is proportional to the displacement from the equilibrium position, the oscillation is called simple harmonic motion. However, not all periodic oscillations are simple harmonic motions.

Consider a ruler with one end fixed to the tabletop and the other free with a mass attached. When this system is pulled up and released, it vibrates.

Here, the acceleration is directed toward the center of oscillation and is proportional to the displacement from the equilibrium position. As a result, the force is proportional to the displacement but in the opposite direction. The proportionality constant is the spring constant.

One complete oscillation is called a cycle, and the time required to complete one cycle is called a period. The number of cycles per unit time is the frequency.

At equilibrium, the net force is zero. The maximum displacement from the equilibrium position is the amplitude.