GregLocock is right, the classical solution shows no power consumption in the steady state, as elastic springs only store, then give back virtually the same energy. Moving mass up/down has the same result. Modern bearings have very little energy consumption.
To find power consumption, we need to determine where the input mechanical energy is being dissipated or moved out of the system.
I would think the primary energy consumption path is the frictional heating of the material in the shaking table, with a secondary energy output of the kinetic energy imparted to the material which exits the shaker. Having said that, the analysis to arrive at the required power becomes very complicated, and probably only available from tests or empirical data for similar equipment.
Since the mass of the system is nearly doubled, you could conservatively expect the starting loads to approximately double. This would indicate a similar 10 HP motor is probably safe from a starting standpoint.
As far a steady state loads, the new wear material may cause different frictional character on the table, and this could change the power consumption. Steady state power requirements could go up or down, and this is unknown. Engineering judgment tells me that the power will probably be less than double the original, so the 10 HP motor is again OK.
