Show that for a particle in linear S.H.M., the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

Explanation

To show that for a particle in linear Simple Harmonic Motion (SHM), the average kinetic energy over a period of oscillation equals the average potential energy over the same period, we can follow these steps:

### Step 1: Understand the equations of SHM
The displacement of a particle in SHM can be described by the equation:
\[ y(t) = A \sin(\omega t) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency.
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