The displacement of particle in S.H.M. May be given by`y = a sin(omegat + phi)`show that if the time t is increased by`2pi//omega`, the value of y remains the same.

Explanation

To show that the value of \( y \) remains the same when the time \( t \) is increased by \( \frac{2\pi}{\omega} \), we start with the given equation of motion for simple harmonic motion (S.H.M.):

\[ y = a \sin(\omega t + \phi) \]

### Step 1: Substitute \( t + \frac{2\pi}{\omega} \) into the equation
We need to find the value of \( y \) when \( t \) is increased by \( \frac{2\pi}{\omega} \). Therefore, we substitute \( t + \frac{2\pi}{\omega} \) into the equation:
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