A mass, m, is supported on a light beam, which is free to rotate about the pivot at O as illustrated in the figure below (note figure is not drawn to scale). The beam is supported by two springs of stiffness, k, and k₂, located at a distance, L and a respectively, from the pivot. Additionally a damper with damping coefficient cis located a distance b from the pivot. A step force of constant magnitude, F(t) = Fo is applied to the mass from time t=0, as illustrated. Using the data below, derive the equation of motion of the system.

Fig: 1

Fig: 2