$($both question$)$ Mechanical Vibration, assignment $1.$ Review of Dynamics, determining the Equation of Motion of a

vibrating system, draw all the FBDs and KDs$.$

Problem $1.$ Derive the equation of motion of the following bar$-$springs system for small rotation of the

bar, assuming the mass of the bar as $m.$ There is a force $F$ applied at the lower end of the bar.

Problem $2.$ Derive the equation of motion of the rolling disk system for small rotation.