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 ${\mathrm{W}}_{\text{ext }}=\mathrm{\Delta }\left(\mathrm{ME}\right); \mathrm{ME}$ = Mechanical energy. Mechanical energy will keep on increasing up to the instant the W_ext 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 ${\mathrm{ME}}_{max}=(1/2){\mathrm{mv}}^2$

At 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, ${\mathrm{ME}}_{max}=(1/2)\mathrm{m}(2\mathrm{u}{)}^2=2{\mathrm{mu}}^2$