This problem is related to Problems 9.33 - 9.38 in the text.
We have solved differential equations using the method of
undetermined coefficients (Chapter 7) and Laplace transforms
(Chapter 8). We can use Fourier series to find the particular
solution of an arbitrary order differential equation - as long as
the driving function is periodic and can be represented by a
Fourier series.
In the problem description and answers, all numerical
angles(phases) should be given in radian angles (not degrees).
Given the differential
equation y′′+4y′+40y=4cos(5t+0.523599)+4cos(7t+1.0472)y″+4y′+40y=4cos(5t+0.523599)+4cos(7t+1.0472) .
This Problem Is Related To Problems 9 33 9 38 In The Text We Have Solved Differential Equations Using The Method Of U 1 (144.24 KiB) Viewed 22 times
(25 points) This problem is related to Problems 9.33 - 9.38 in the text. We have solved differential equations using the method of undetermined coefficients (Chapter 7) and Laplace transforms (Chapter 8). We can use Fourier series to find the particular solution of an arbitrary order differential equation - as long as the driving function is periodic and can be represented by a Fourier series. - In the problem description and answers, all numerical angles(phases) should be given in radian angles (not degrees). Given the differential equation V" + 4y + 40y = 4cos(5t + 0.523599) + 4cos(7t + 1.0472) = a. Write the fundamental frequency that you will use for this system. W. = help (numbers) b. Write the transfer function for this system as a function of n. (See page 530 of the text.) H(n) = help (formulas) C. Find the particular solution, yp(t). No step function in this answer. Note the accuracy is 0.01% relative error. If the numbers of small, that means you need more decimal places to get the right answer. yp(t) = help (formulas)
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