$(17)$ witite down the differential equations of motion for the following cases $($Refer Fig.$)$

$($i$)$ Spring mass system on an inclined plane.

$($ii$)$ Simple pendulum.

$($iii$)$ Simple pendulum with spring

$($iv$)$ Light cantilever with end mass

$($v$)$ Compound pendulum

$($vi$)$ Torsional Pendulum

$($vii$)$

Prob. $74($ii$)$

Prob$\mathrm{.}74($v$)$