Problem

The mechanism consists of a disk D pinned at G, which is both the geometric center of the...

The mechanism consists of a disk D pinned at G, which is both the geometric center of the disk and its mass center. The outer circumference of the disk has radius ro = 0.1 m and is connected to an element consisting of a linear spring with stiffness k1 = 100 N/m in parallel with a dashpot with damping coefficient c = 50 N·s/m. The disk has a hub of radius ri = 0.05 m that is connected to a linear spring with constant k2 = 350 N/m. Knowing that for θ = 0 the disk is in static equilibrium and that the mass moment of inertia of the disk is IG = 0.001 kg·m2, derive the linearized equation of motion of the disk in terms of θ. In addition, calculate the resulting vibrational motion if the system is released from rest with an initial angular displacement θi = 0.05 rad.