The spring with a stiffness of 400 N / m was compressed by 5 cm. What work was done in this case?

The spring with a stiffness of 400 N / m was compressed by 5 cm. What work was done in this case? What is the maximum speed of a body attached to the end of a spring as a projectile? What work did the elastic force do when the spring returned to its original size?

The work performed when the spring is compressed with a stiffness k:
A1 = k x ^ 2/2,

where x is the magnitude of the compression deformation x = 5 cm = 0.05 m.

A1 = 400 × 0.05 ^ 2/2 = 0.50 J.

When the spring returns to its original size, the elastic force performs work equal to the work performed in compression, that is, A2 = A1 = 0.50 J.
The work of the elastic force is equal to the kinetic energy of the body attached to the spring:
A2 = Ek = M V ^ 2/2,

where M is body weight, kg.

Then the maximum speed of the body: V = (2 A2 / M) ^ 1/2.