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Chem Differential Eq HW Solutions Fall 2011 24

Chem Differential Eq HW Solutions Fall 2011 24 - 24 Chapter...

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24 Chapter 2 Fourier Series The modified steady-state is obtained by subtracting y 3 from the steady-state. Here is its graph. modifiedsteadystate t_ steadystate t alph 3 Cos 3t bet 3 Sin 3t ; Plot Evaluate modifiedsteadystate t , t,0,4Pi 2 4 6 8 10 12 -0.1 -0.05 0.05 0.1 In order to compare, we plot both functions on the same graph. Plot Evaluate steadystate t , modifiedsteadystate t , t,0,4Pi 2 4 6 8 10 12 -0.4 -0.2 0.2 0.4 It seems like we were able to reduce the amplitude of the steady-state solution by a factor of 2 or 3 by removing the third normal mode. Can we do better? Let us analyze the amplitudes of the normal modes. These are equal to α 2 n + β 2 n . We have the following numerical values:
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