Asonobuoy (sound-measuring device) floats in a standing wave tank. The device is a cylinde...

Asonobuoy (sound-measuring device) floats in a standing wave tank. The device is a cylinder of mass m and cross-sectional area A. The water density is p, and the buoyancy force supporting the buoy equals the weight of the water that would occupy the volume of the part of the cylinder below' the surface. When the water in the tank is stationary, the buoy is in equilibrium in the vertical position shown at the left. Waves are then generated in the tank, causing the depth of the water at the sonobuoy's position relative to its original depth to be d = d0 sin ω0t. Let y be the sonobuoy’s vertical position relative to its original position. Show that the sonobuoy’s vertical position is governed by the equation