Question

In the previous illustration. Consider the situation when the string is completely compressed. Then it begins to relax and will come to its original length.
a. What is the work done by the spring during the period?
b. Is the work done by the spring positive or negative?

Answer 1

Work done by the spring force.
`W_(spring)=-1/2k(x_f^2-x_i^2)`
`=-1/2k(0-x_0^2)=1/2kx_0^2`

From previous problem, `x_0=v_0*sqrt(m/v)`
Hence, `W_(spring)=1/2k(v_0sqrt(m/k))^2=1/2mv_0^2`