A pendulum consists of a mass m suspended by a massless spring with un-extended length b and spring constant k. The point of support of the pendulum is moving horizontally with acceleration a. Find the pendulum's equation of motion for variable ? by using the Lagrangian dynamics. Suppose that the spring remains straight and extends only along its length, ? is the instantaneous length.

A pendulum consists of a mass m suspended by a massless spring with un-extended length b and spring constant k. The point of support of the pendulum is moving horizontally with acceleration a. Find the pendulum's equation of motion for variable ? by using the Lagrangian dynamics. Suppose that the spring remains straight and extends only along its length, ? is the instantaneous length.