Pendulum Problem (Solve with SIMULINK) Consider a simple pendulum having length L, mass m, and instantaneous angular displacement (theta), as shown below in Figure 1. The force equation for pendulum is 2 2 d sin 0 d mg mL t = Thus 2 2 d sin d g t L = . For all angles , we make the assumption that sin = leading to an analytical solution. However, for large angles , we resort to a numerical method to solve the differential equation above. We fi rst reduce the second-order differential equation to a set of two fi rst-order differential equations by introducing (angular velocity), thus d d d sin( ) d t g t L = = FIGURE 1 mg Pendulum swing. mL d2 /dt 2 L