A sphere of solid density rho s and diameter D is dropped to a water pond (density rho s and viscosity mu). Initial vertical displacement is x(t=0) = 0 and initial velocity is v(t=0) = 0. Derive the governing differential equation for the motion. Solve the equation using Laplace Transform. Derive the terminal velocity v0 when acceleration becomes zero. Derive the characteristic relaxation time t* in terms of all given variables.