A particle of mass 0.50 kg executes a simple harmonic motion under a force `F=-(50Nm^-1)x`. If it crosses the centre of oscillation with a speed of `10ms^-1`, find the amplitude of the motion.

Explanation

To solve the problem, we will use the principles of energy conservation in simple harmonic motion (SHM). The total mechanical energy in SHM is conserved and can be expressed in terms of kinetic energy and potential energy.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of the particle, \( m = 0.50 \, \text{kg} \)
- Speed at the center of oscillation, \( v = 10 \, \text{m/s} \)
- Force constant (spring constant), \( k = 50 \, \text{N/m} \)
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