Beam Driven by Two Wheels, Solution

The (angular) frequency is given by

To find this result one introduces the normal forces F_n1 and F_n2 of the wheels, the weight F_g = m g and the inertial force F_i = m .

The force balance gives

The torque balance around the two contact points A and B is

Solving (2) and (3) for the normal forces and inserting them into (1) one immediately gets