Derive the equation of motion for a uniform stiff rod restrained from vertical motion by a torsional spring of stiffness \(K\) and two translational springs each of stiffness \(k\), as shown in Figure 2.46. The torsional spring constant is determined by the application of a moment \(M\) and the measurement of the angular displacement \(\theta\), that is, \(M=K \theta\). Calculate the natural frequency of oscillation. Let \(J\) be the mass moment of inertia of the rod about the left restraint. State any assumptions.

Transcribed Image Text:

K Figure 2.46: Restrained rigid rod. k