For a simple pendulum of length l, the angle theta between rest position and deflected position is the only generalized coordinate. Kinetic energy of the bob of mass m is T = 1/2 ml2 theta prime2, and its potential energy, V = mgl (1- Cos theta). Display the Lagrangian, L of this system, and hence determine the equation of motion for the simple harmonic motion for the smal angle theta.

For a simple pendulum of length l, the angle theta between rest position and deflected position is the only generalized coordinate. Kinetic energy of the bob of mass m is T = 1/2 ml2 theta prime2, and its potential energy, V = mgl (1- Cos theta). Display the Lagrangian, L of this system, and hence determine the equation of motion for the simple harmonic motion for the smal angle theta.