A uniform rigid and massless rod is pinned at one end and connected to ground via a spring at the other end. At midpoint on the rod, a spring is connected to a mass which is connected to a fixed point via another spring, as shown in Figure 2.47.

(a) Derive the equation of free vibration for the system.

(b) Find the natural frequency.

(c) Calculate the natural frequency given the following parameters: \(k_{1}=20 \mathrm{lb} / \mathrm{in}, k_{2}=30 \mathrm{lb} / \mathrm{in}, k_{3}=40 \mathrm{lb} / \mathrm{in}\), \(m g=50 \mathrm{lb}\), and \(l=8 \mathrm{ft}\).

Transcribed Image Text:

p 1/2- -6000- m 6000- k k B 1/2- Figure 2.47: A coupled rod-mass system. k