Problem $1(20$ points$)$: Consider the following system:

A$.$ Find the equations of motion for each mass in the system in the time domain and the

Laplace domain. All masses have mass $m,$ all springs have spring constant $K,$ and the

springs are at their natural length at start.

$($Hint: You only need the equations for the $0$th mass, the i$-$th mass, and the $(n+1)-$th

mass.$)$

B$.$ Sum all the Laplace equations to find a single Laplace equation that describes a

relationship between the locations of the $0$th mass and the $(n+1)-$th mass.

C$.$ Assuming $m$ is negligible, what is the relation between $x_0$ and $x_{n+1}?$