Problem $3(25$ Points$)$:

$F=-kx=-k(x_0-x)$

A mass$-$spring$-$damper system is shown right. The coordinate

origin is at the static deflection $($so omit force due to gravity$).$

All the springs in the cluster have the same constant $k_2.$

$($a$)$ Find the equivalent spring stiffiness in the cluster in terms

of $k_2.$

$($b$)$ Find the equations of motion of the system.

$($a$.)$