A pendulum of negligible mass is connected to a spring of stiffness k at halfway along its length, l, as illustrated in Figure. The pendulum has two masses fixed to it: one at the connection point with the spring and one at the top.
Derive the equation of motion using the Lagrange formulation, linearize the equation, and compute the system's natural frequency.
Assume that the angle remains small enough so that the spring only stretches significantly in the horizontal direction.
