17.2 Simple Harmonic Motion

Definition

Conditions: Simple Harmonic Motion

A motion is said to be Simple Harmonic if:

• The acceleration is directly proportional to the displacement.
• The acceleration and displacement are in opposite directions.

Equation

Mathematically,

$$\begin{array}{rl}a& \propto -x\\ a& =-kx\\ a& =-{\omega }^{2}x\end{array}$$

The equation defining Simple Harmonic Motion is:

$$\boxed{a=-{\omega }^{2}x}$$

Key Point: Negative Sign

The negative sign int he equation indicates that the acceleration, and therefore the restoring force, is always in the opposite direction to the displacement. For example,

• If the body is moving right, the force pulls the body to the left.
• If the body is moving left, the force pulls the body to the right.