Let x be the height of the cylinder from the bottom of the vessel; you should obtain an expression for the kinetic energy in the form T=a\frac {\dot x^2}x, where \dot x=\frac {\mathrm dx}{\mathrm dt}, and a is a constant. Now there are two ways to proceed. First, you can express \mathrm dt from the energy conservation law T+K=E_0 in terms of \mathrm dx and integrate. Second and mathematically simpler way is to substitute x=\xi^2 to obtain a nice equation for \ddot \xi.

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