Problem. Your job is to move a mass suspended on a pendulum from one point in space to another in as short a time as you can, with the least oscillations you can.

Objectives:

  1. Solution of the differential equation via Laplace transforms
  2. Analysis of different solutions with different forcing functions that achieve the goal.
  3. Plot some trajectories using MATLAB, Mathematica, Excel, or ???
  4. Written description and explanation of your work.

Organization. Your paper should be organized as follows.

  1. Introduction.Provide a succinct statement of the problem.
  2. Solution analysis.How did you perform the computations/experiments/etc that led to the answer?
  3. Results. Here you will experiment with some forcing functions to what the oscillation amplitudes look like and how long it takes the crane to move the mass.We should see some graphs here.
  4. Discussion.How do you interpret your results? What else might be done?
  5. Literature Cited.If you use any references, please list them here.If no references were needed, you may omit this section.

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