A block of mass one kg is fastened to a spring with a spring constant `50Nm^(-1)`. The block is pulled to a distance `x=10cm` from its equilibrium position at `x=0` on a frictionless surface from rest at `t=0. ` Write the expression for its x(t) and v(t).

Explanation

To solve the problem, we need to derive the expressions for the displacement \( x(t) \) and the velocity \( v(t) \) of a block attached to a spring undergoing simple harmonic motion (SHM).

### Step-by-Step Solution:

1. **Identify the parameters:**
- Mass \( m = 1 \, \text{kg} \)
- Spring constant \( k = 50 \, \text{N/m} \)
- Initial displacement \( x_0 = 10 \, \text{cm} = 0.1 \, \text{m} \)
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