Coupled Mass$-$Spring$-$Damper System:

a$)$ Use the information below to derive the system of linear second order

ordinary differential equations governing the circuit.

b$)$ Let

$m_1,=2kg,m_2=3kg$

$k_1,=50\frac{N}{m},k_2=30\frac{N}{m},k_3=40\frac{N}{m}$

$c_1,=5N\frac{s}{m},c_2=2N\frac{s}{m}$

Then, by means of Laplace transform methods, determine

the system's displacement and velocity.