Module 3 - Constrained engineering systems

Pendulum motion

1. Creating equations of motion

   1. draw a Free body diagram

   2. draw a Kinetic diagram

   3. use kinematic constraints to create the equations of motion for the system

2. Solving equations of motion

   1. Derive and define a set of linear differential equations e.g.

      • \(\ddot{x} = -\omega^2 x\)

      • \(\ddot{x} = \lambda x\)

      • \(\ddot{x} = constant\)

   2. Solve this set of linear differential equations

   3. Derive and define nonlinear differential equations

   4. Use computational methods to solve nonlinear differential equations