Part $1(10$ Points$)$: A mass $($ m $)$ is first located at the uncompressed length $($l$)$ of two springs

as shown above. Please find the equilibrium position of the mass $($ m $)$ for this system, and

clearly illustrate this position as a vector.

Part $2(10$ Points$)$: Find the equation of motion of the system for motion around the

equilibrium position identified in Part $1.$

Part $3(10$ Points$)$: Please determine when the system in Part $2$ will be underdamped.

Part $4(10$ points$)$: If the stiffness of both springs is decreased by half how will the damping

ratio change?

Part $5(10)$: If the underdamped system is released from the original configuration shown in

the illustration above please find the position of the particle as a function of time.

solve each part