In the ride shown, a person A sits in a seat that is attached via a cable of length L to a...

In the ride shown, a person A sits in a seat that is attached via a cable of length L to a freely moving trolley B of mass mB. The total mass of the person and the seat is mA. The trolley is constrained by the beam to move in only the horizontal direction. The rider is released from rest at the angle θ = θ0 and is allowed to swing in the vertical plane. Neglect the mass of the cable, and treat the person and the seat as a single particle.

Figure P3.113

Derive the system’s equations of motion, using the position of the trolley and the angle θ as dependent variables.