1. The mass m shown is attached to rigid rod having an inertia / about the pivot and negligible pivot friction. The input is the displacement z. When z =0=0, the spring is at its free length. Assuming that is small, (a) Derive the equation of motion for with z as the input. (b) Obtain the expression for the natural frequency. (c) Obtain the expression for the damping ratio. KL +mgL, Answer: @= √ mL +I H m