Consider an ideal spring that obeys Hooke’s law and offers a restoring force F=−kx. The spring is made to change its length smoothly from extension x1 to extension x2(x2>x1) along a straight line on a smooth horizontal surface.
a. (i) Derive an expression for the work done by the spring force during this change of length.
b. (ii) A spring with k=150Nm−1 is already stretched by x1=10cm. It is further stretched to x2=15cm. Using your result from part (i), compute (a) the work done by the spring force and (b) the work done by an external agent that performs the stretching slowly.