A partical of mass `0.2 kg` undergoes SHM according to the equation `x (t) = 3 sin (pi t + pi//4)`.
i. What is the total energy of the partical if potential energy of zero at mean position ?
ii. What are the kinetic and potential energies of partical at time `t = 1 s`?
iii. At what time instants is the particals energies purely kinetic?

Explanation

To solve the problem step by step, we will break it down into three parts as per the question.

### Given Data:
- Mass of the particle, \( m = 0.2 \, \text{kg} \)
- Displacement equation: \( x(t) = 3 \sin(\pi t + \frac{\pi}{4}) \)

### Part (i): Total Energy of the Particle

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