Problem 1 – Hint 3

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.

Please submit the solution to this problem via e-mail to The next hint for the Problem 1 will be published alongside with the Problem No 2 at 13:00 GMT, 18th December 2022, together with the next updates of the intermediate results.