The potential energy of a particle of mass m is given by `U(x)=U_0(1-cos cx)` where `U_0` and c are constants. Find the time period of small oscillations of the particle.

Explanation

To find the time period of small oscillations of the particle given the potential energy function \( U(x) = U_0(1 - \cos(cx)) \), we can follow these steps:

### Step 1: Find the Force
The force \( F \) acting on the particle can be derived from the potential energy function using the relation:
\[ F = -\frac{dU}{dx} \]
Calculating the derivative of \( U(x) \):
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