• Obtain equations of motion for the mechanical system shown in Figure 3.9 of the text. Simply the equation of motion by eliminating all internal forces, and Theta2.
• Place the equations of motion from the previous step into state space format for nonlinear systems. Use the following state variable assignements:
  q1=xdot
  q2=theta1dot
  q3=x
  q4=theta1
  
• Find the equilibrium values of the displacements x and theta1.
• Linearize the nonlinear spring and damper about their equilibrium "displacements".
• Assign state variables to the perturbation displacements and their derivatives. Use the following state variable assignments:
  q1=x_hat_dot
  q2=theta1_hat_dot
  q3=x_hat
  q4=theta1_hat
  
• Place the linearized state equations into standard format for linear state space systems. Do not specify an output y (no C^T and d matrices).
• Simulate the nonlinear and linear systems over the time range 0-200 sec with a time step of 2 sec using ode45. Plot each state variable versus time as computed from the nonlinear and linearized system together on the same graph.

Due Monday October 23 2000