• In these systems there are some basic steps to solving the problems,
1. Assign letters/numbers to designate components (if not already done) - this will allow you to refer to components in your calculations.
2. Define a position and directions for any moving masses. This will include the selection of reference points.
3. Draw free body diagrams for each component, and add forces (inertia is optional).
4. Write equations for each component by summing forces.
5. Combine the equations by eliminating unwanted variables.
6. Develop a final equation that relates input (forcing functions) to outputs (results).
• Develop the equation relating the input force to the motion of the cart for the problem below. Assume that in the initial position the spring is compressed a distance ’d’.
• Develop the equation relating the input force to the motion (in terms of ’x’) of the lefthand cart for the problem below.
• Consider the examples below,
• In the previous example not the similarity between springs/resistors in series/parallel.