shows a uniform rigid bar of mass m and length 1, pivoted at one end (point 0) and carrying a circular disk of mass M and mass moment of inertia / (about its rotational axis) at the other end (point P). The circular disk is connected to a spring of stiffness k and a viscous damper of damping constant c as indicated.
a. Derive the equation of motion of the system for small angular displacements of the rigid bar about the pivot point O and express it in the form: тов + сов + καθ=0
b. Derive conditions corresponding to the stable, unstable, and marginally stable behavior of the system.