Consider the system of Figure P12.36.

(a) Derive the nonlinear differential equations governing the motion of the system using the generalized coordinates shown.

(b) Expand trigonometric functions of the generalized coordinates using Taylor series expansions. Rewrite the differential equations keeping only quadratic and cubic nonlinearities.

(c) For what values of \(l\) in terms of the other parameters will an internal resonance exist?

(d) In the absence of an internal resonance, for what values of \(\omega\) will resonance conditions exist?

Transcribed Image Text:

k m FIGURE P12.36 X F(t) = Fo sinot Slender rod of mass m