University of Florida/Egm4313/s12.team8.dupre/R5.4

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Problem 5.4

Problem Statement[edit]

(1) Show that:

(5.1)

is indeed the overall particular solution of the L2-ODE-VC:

(5.2)

with the excitation:

(5.3)

(2) Discuss the choice of in the above table , e.g., for:



Why would you need to have both in ?

Solution (1)[edit]

Using the following equation:

(5.4)

for different r and y values gives us the following:

(5.5)

(5.6)

(5.7)

Now, adding (5.4),(5.5), and (5.6), gives us:

(5.8)

Equation (5.8) shows us that the overall particular solution of (5.2) with excitation (5.3), is in fact, equation (5.1).

Solution (2)[edit]

We know that the given example for an excitation is the periodic excitation:



When we decompose a periodic excitation into a Fourier trigonometric series, we find:



Since we know that the particular solution should depend on the excitation, we know that for a periodic excitation , we would need both in to obtain the correct particular solution.