To prove that in Simple Harmonic Motion (SHM), the acceleration of a body is proportional to its distance from the equilibrium position and directed towards that position, we can start by considering the general properties of SHM.
### Derivation:
1. **Definition of SHM**:
In SHM, the displacement \( x \) of the body from its equilibrium position is a function of time that can typically be represented as:
\[
x(t) = A \cos(\omega t +