1. The problem statement, all variables and given/known data A small ball with mass M attached to a uniform rod of mass m and length l pivoted at point o and attached to two springs with spring constant k1 and k2 at distance d1 and d2 from point o as shown in Fig 2. The system oscillates around the horizontal line. Assume the system is in a fluid and is damped by a viscous drag force proportional to the speed. Find the equation of motion for the small angle oscillation and its solution if it starts from rest with initial angular position θ0. Find the quality factor. Ignore the buoyancy force. 2. Relevant equations Moment of inertia for rod: Irod = (1/3)*m*l2 Moment of inertia for ball: Iball = M*l^2 Equation for torque: τ = I*θ'' Drag force: FD = -b*cosθ Spring force: FS = -k*sinθ Small angle approx for sin: sinθ = θ and for cos: cosθ = 1 3. The attempt at a solution My attempt involves trying to convert all forces to torques and to get an equation of motion in terms of theta. I'm having trouble in a few places. For one, I'm not sure how to handle finding the center of mass symbolically without knowing the mass of the rod. It seems like the CoM could be almost anywhere on the rod, depending on the rod's mass... and the placement of CoM with respect to d1 and d2 seems important. If I can figure out how to set the differential equation up, I don't think solving it will be much trouble.