Question $3$:

As shown in Figure $3,$ a pan of negligible mass is attached to two identical springs of stiffness $\backslash ($ k$=250\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$ in the vertical plane. Initially, each spring has a tension of $50$ N at a horizontal position. A $10$ kg box is dropped from a height of $0\mathrm{.}5$ m above the pan and pushes the pan downwards.

Determine the speed of the pan when the vertical displacement of the pan is $\backslash ($ d$=0\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash ).($Ignore the size of the pan and box. the weight of the springs and any friction.$)$