Tha particle is executing SHM. The amplitude of motion is a. State those positions of the particle in terms of a when (i) the K.E. of the particle is zero (ii) P.E. is zero (iii) P.E. is one-fourth of the total energy (iv) P.E and K.E. are equal.

Explanation

To solve the problem step by step, we will analyze each part of the question regarding a particle executing Simple Harmonic Motion (SHM) with amplitude \( a \).

### Given:
- Amplitude of motion: \( a \)
- Total Energy (E) in SHM: \( E = \frac{1}{2} m \omega^2 a^2 \)
- Kinetic Energy (K.E.): \( K.E. = \frac{1}{2} m \omega^2 (a^2 - y^2) \)
- Potential Energy (P.E.): \( P.E. = \frac{1}{2} m \omega^2 y^2 \)

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