A force F is exerted on a body of mass M, which is connected to a spring (spring constant k). The body has a constant acceleration a. Calculate the work done by the external force in moving the body by a distance D.

Explanation

From force equation, the value of external force at any instant of time, `F=kx+ma`, where x is free end displacement of the string at that time.
Since variable force is involved, let us take small displacement `dx`.
The work done by the force at that time,
`dW=Fdx=(kx+ma)dx`
On integrating,
`W=1/2KD^2+(ma)D`