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MCE 464 Vibrations
Working Model Computer Assignment # 1
One Degree of Freedom, Damped Vibration

Recall homework assignment # 3-4 on page 185 of Rao's text (text figure below)

You were asked to develop the equation of motion

for the system shown. This assignment involves using Working Model to construct this problem, and compare the computer solution with the analytical solution. Remember that the angular displacement theta is measured from the static equilibrium position. In order to do the comparison, use the specific underdamped case with system parameters: m = 10kg, l = lm, k = 500N/m, and c = 200 N-s/m. Choose your own appropriate initial conditions.

  1. Construct the Working Model system with an output window of angular displacement vs time.

  2. Run a WM simulation with the given system parameters. Save a printed screen dump version of a typical run after sufficient time to demonstrate the system response.

  3. Save your typical run data in Excel and plot theta vs t. Quantitatively compare the WM output in the Excel spreadsheet (or in the plot) with the analytical solution. Remember that you can use Excel to calculate the exact analytical solution for ease of comparison. Explicitly compare the damped frequency and the amplitude response.

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