Problem 1: A uniform disk of radius r and mass md rolls without slipping on a cylindrical surface and is attached to a uniform slender bar AB of mass m. The bar is attached to a spring of constant K and can route freely in the vertical plane about point A as shown in the figure.
If the bar AB is displaced by small angle θ and released, determine
a. The energy of the system in terms of θ and θ.
b. The equation of motion in terms of θ and θ using Larange's equations.
c. The natural frequency of vibration of the system.
