A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates horizontally with a position given by x = A cos (wt), as shown below. Use 0 (the angle of the pendulum as measured from the vertical) as your generalized coordinate. In HW 8, you found the Lagrangian of this system is: 1 L = ·m (1² j² + x² + 2lxė cos 0 ) + mgl cos 0 m Use the Euler-Lagrange equation to find the equation of motion for this system. Then make a small angle approximation cos 0 ~ 1. The equation you find should be recognizable as the equation for a driven oscillator. What is the solution for 0 (t) in the small angle approximation?

A pendulum consists of a mass m and a massless stick of length l. The pendulum support oscillates horizontally with a position given by x = A cos (wt), as shown below. Use 0 (the angle of the pendulum as measured from the vertical) as your generalized coordinate. In HW 8, you found the Lagrangian of this system is: 1 L = ·m (1² j² + x² + 2lxė cos 0 ) + mgl cos 0 m Use the Euler-Lagrange equation to find the equation of motion for this system. Then make a small angle approximation cos 0 ~ 1. The equation you find should be recognizable as the equation for a driven oscillator. What is the solution for 0 (t) in the small angle approximation?