Question: For a pendulum supported from a horizontally restrained mass, as shown in Figure 5.39, derive the governing equations of motion using (a) Lagrange's equation and

For a pendulum supported from a horizontally restrained mass, as shown in Figure 5.39, derive the governing equations of motion using

(a) Lagrange's equation and

(b) Hamilton's principle. Identify the constraint equations. Discuss the effect of setting $m_{1}=0$. Finally, simplify the governing equations if small motions are assumed.

m -Static equilibrium m x 0 X2 k m m2 F(1) Figure

m -Static equilibrium m x 0 X2 k m m2 F(1) Figure 5.39: Pendulum suspended from a horizontally restrained mass.

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