The L-shaped bar lies in the vertical plane and is pinned at O. One end of the bar has a l...

The L-shaped bar lies in the vertical plane and is pinned at O. One end of the bar has a linear elastic spring with constant k attached to it, and attached at the other end is a mass m of negligible size. The angle θ is measured from the equilibrium position of the system and it is assumed to be small.

Assuming that the L-shaped bar has mass per unit length ρ, determine the natural period of vibration of the system by writing the Newton-Euler equations.

Figure P9.12