In the given figure, the system is in the static equilibrium position. The mass $m$ is connected to

a fixed ground with the spring $k,$ and connected to a table that moves $y(t)=$Ysin$t$ with the

damping element $c.$

longleftarrow

a$)$ Obtain the differential equation of the system using the Lagrange method.

b$)$ Obtain the differential equation of the system using Newton's $2^{nd}$ Law.