Question $5$:

In Position $1$ on the smooth bar, the $5-$kg collar has a downward velocity of $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ and the spring is unstretched. The spring constant is $\backslash (\backslash$mathrm$\{$k$\}=100\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ What maximum downward velocity does the collar attain as it falls? Hint: how do you find a mathematically find a maximum $($or minimum$)?$