The initial analysis all comes down to how our drivers, or cylinders, will behave when all of the parameters are established. In order to do that, the used the equation seen below in Figure 3.

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Figure 3: Formula for Displacement of Cylinder

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Since this equation is given as a function of time, the program calculates this value in a tabular format. The same formula is repeated to find the cylinders amplitude with a different value of time within the table as seen in Table 2.

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Table 2: Amplitude and Velocity of Driver

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With these table values, Excel plots the data in a graph that can be seen in Figure 4. Since the data points in the graph are largely dependent on time, it is important to keep a constant, small change in time from point to point. If the change in time is too large, the amplitude of the cylinder may not show as a smooth curve. Therefore, it is important to be mindful of the time-step because the smaller, the more accurate and smooth a curve.

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Figure 4: Amplitude of Driver (Measured in Meters)

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The program then calculates the velocity of the cylinder. It does so by using the same method as finding the amplitude except in this case, the derivative of the amplitude function is used. Again, this is largely affected by the time-step of the table and it is crucial to be using as small a time-step as reasonable to find accurate values. To find the period of oscillation of the cylinder, Excel locates the time at which the amplitude of the cylinder again reaches its max value after 0 seconds. Since the cylinder starts off at it max, it’s safe to assume that the next time it reaches a max will be the time for a period. The frequency of the cylinder is simply 1 over the time taken for a period.

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