Exercise 2: Pendulum is widely used in the traditional clock. It has a weight suspended from a
pivot point by a massless cord. The weight has mass of m, the length of cord is L, T is the
applied torque at moment t=0 (input), $\theta$ is the angle that pendulum swings away from vertical.
Assume there is no friction in this process and zero initial conditions.
(1) According to Newton's law for rotational motion, $M = I\ddot{\theta}$, where M is the sum of
external moments, I is the mass moment of inertia ($I = mL^2$ for the ball), $\ddot{\theta}$ is the angular
acceleration, write the dynamic model of pendulum. Assume the motion is small enough
that $sin\theta \approx \theta$. (Hint: The torque generated from gravity is opposite direction to the
applied torque.)
(2) If m = 1kg, L=1m, g = 9.81 m/s², T is unit step input. Use Simulink to find the response.
(3) Find the transfer function of the system, use the same parameter, find the response of the
system using command lines. Compare the results.
