4. Now consider the undamped version of (0.1), with forcing term F(t): = cos ßt, mu" = -ku + cos Bt. (0.4) Using the method of undetermined coefficients, find a particular solution to the equation (0.4). Then find the general solution of equation (0.4). Assume that ß> 0 and that is different from the natural frequency of the oscillator, that is, ß # √√k/m. You must show all of your work t A particular solution of (0.4) is U (t) = The general solution of (0.4) is u(t) =
4. Now consider the undamped version of (0.1), with forcing term F(t): = cos ßt, mu" = -ku + cos Bt. (0.4) Using the method of undetermined coefficients, find a particular solution to the equation (0.4). Then find the general solution of equation (0.4). Assume that ß> 0 and that is different from the natural frequency of the oscillator, that is, ß # √√k/m. You must show all of your work t A particular solution of (0.4) is U (t) = The general solution of (0.4) is u(t) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. Now consider the undamped version of (0.1), with forcing term F(t) = cos ßt,
(0.4)
mu"
=-ku + cos Bt.
Using the method of undetermined coefficients, find a particular solution to the equation (0.4).
Then find the general solution of equation (0.4). Assume that 3 > 0 and that is different from
the natural frequency of the oscillator, that is, ß ‡ √k/m.
You must show all of your work †
A particular solution of (0.4) is U(t) =
The general solution of (0.4) is u(t) =
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