Problem $1$:

Consider two masses suspended on springs as shown below.

Figure $1$: Two masses on a spring

a$)$ Set up a model for the $($undamped$)$ system by obtaining the equation of motion for each mass

b$)$ Transform the model into a system of first order ODEs

c$)$ Obtain the general solution to the system of ODEs by assuming

$y=x{e}^t,$ such that $,={}^2$