1) A long cylindrical rod of radius, r is weighted on one end so that it floats upright in a fluid having a density. It is pushed down a distance x from its equilibrium position and released. Show that the rod will execute simple harmonic motion if the resistive effects of the fluid are negligible and determine the period of the oscillations>> Start with the forces: mg and the "restoring" force, bouyancy. Bouyance is dependent on displacement. mg- restoring force = mass*acceleration where acceleration is d"x/dx". BUT, how does that lead me to showing the rod will execute simple harmonic motion? and how do i go about determining period of oscillations from there?