Consider the system shown in Figure $6,$ which is a crude model of a person seated on a swing. The

swinger's input is modelled as a torque $T(t)$ applied to the three$-$mass body as shown in the figure ${?}^1.$

You may assume that all the rods have negligible mass and note that gravity acts as shown in the

diagram. Derive the equations of motion using the Newton$-$Euler approach. Be sure to draw any

necessary free body diagrams and use the $xyz$ coordinate system $($fixed in space, origin at $O)$ in your

analysis.