Consider the pendulum system shown in Figure 3.16, where the input is the horizontal force u(t) and the output is the angular displacement θ. It is assumed that there is no friction in the hinge and no air resistance. Find a differential equation to describe the system. Is the equation a linear equation? If θ is small so that sin θ and cos θ can be approximated as θ and 1, respectively, what is its differential equation?
