Equation of motion of a beam pivoted in the middle that has a piston at either end?

Question

How do you derive the equation of motion of a beam pivoted in the middle? At each end there is a piston. The pistons have a mass. Where does the mass of the pistons come into the equation?

Answer 1

The pistons must move up and down in simple harmonic motion. You don't need the masses. All you want to do is write the kinematic equation. That is the description of the movement, not the forces involved.