b$)$ Consider the structural system presented in Figure Q$2.$ By taking the vertical displacement of the right mass as the degree of freedom of reference, determine its equation of motion and its period.

$[10$ marks$]$

c$)$ What is the condition for a stable response of the system in Figure Q$2$ under free vibrations?

$[5$ marks$]$

Make appropriate assumptions for any missing information and state them clearly in your solutions.