A particle of mass `m` executes `SHM` with amplitude 'a' and frequency 'v'. The average kinetic energy during motion from the position of equilibrium to the end is:
(1) `2pi^(2) ma^(2) v^(2)` (2) `pi^(2)ma^(2) v^(2)`
(3) `(1)/(2) ma^(2) v^(2)` (4) `4pi^(2) ma^(2) v^(2)`

Explanation

To find the average kinetic energy of a particle of mass \( m \) executing simple harmonic motion (SHM) from the equilibrium position to the end of its motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kinetic Energy in SHM**:
- In SHM, the kinetic energy (KE) at any position can be expressed as:
\[
KE = \frac{1}{2} m v^2
...