A mass of 0.5 kg is hung from a spring. A gradually increasing 0.5 N force is required to pull the mass downward a distance of 0.25 m from its equilibrium position,if the mass is then released from this position, find
(a) The total energy of the system .
(b) The frequency of the oscillation
(c ) The speed and acceleration of the mass as it passes the equilibrium position.
(d) The speed and acceleration of the mass when the diplacement from equilibrium is 0.25 m
(e) For the initial condition stated, write down the diplacement equation of motion for this mass.

Explanation

Let's solve the problem step by step.

### Given Data:
- Mass, \( m = 0.5 \, \text{kg} \)
- Force applied, \( F = 0.5 \, \text{N} \)
- Displacement from equilibrium, \( x = 0.25 \, \text{m} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

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