A block attached with a spring is kept on a smooth horizontal surface. Now the free end of the spring is pulled with a constant velocity u horizontally. Then the maximum energy stored in the spring and block system during subsequent motion is

As Wext =Δ(ME); ME = Mechanical energy. Mechanical energy will keep on increasing up to the instant the Wext is positive, which will happen till there is no compression in the spring.First the spring gets extended to a maximum and after which the extension decreases up to the natural length. After that there is a compression in the spring, results in a -ve external work (so as to move the end of spring at constant speed u). Hence, maximum energy stored is at the natural length and MEmax=(1/2)mv2At the natural length v = 2u, since the block is moving at this instant at a speed u with respect to the other end of the spring. Hence, MEmax=(1/2)m(2u)2=2mu2