Coupled Pendulums with Damping:

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

differential equations.

$m,=1kg,l=1m$

$g,=9\mathrm{.}81\frac{m}{s^2},k=20\frac{N}{m}$

$c,=0\mathrm{.}1N\frac{s}{m}$

b$)$ Hence, by means of matrix and Laplace transform methods, find the

displacement of pendulum $1$ and pendulum $2.$