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2. In the mechanical system shown in Fig. 2, assume that the rod is massless, perfectly rigid, and pivoted at point P. The mass of the small ball is m, the stiffness of the spring is k, and the damping cocfficient of the dashpot is c. The displacement r is mcasured from the horizontal position, where the spring is undeformed. Initially, the system is at rest and the spring is undeformed (a) Assume that the displacement z is small. Derive the cquation of motion governing the (b) Determine the undamped natural frequency wn and viscous damping factorof the (c) If k-100 N/m, c = 5 Ns/m, m = 1 kg, a-1 m, and b 2 m, determine if motion r and the initial conditions. system the system is overdamped, underdamped, or critically damped. Justify your answer, and roughly sketch the impulse response function. (Plcase dont calculate the impulsc response function.)What is the final displacement x of the lever (i.e., after the transient response has died out)? Docs it depend on whether the system is overdamped or underdamped? Why?Figure 2: A massless mechanical lever

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