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In each of Problems 7 through 10, find the steady periodic so- lution xsp (1) = C cos(oot - a) of the given equation mx" + ex' + kx = F(t) with periodic forcing function F(t) of fre- quency o. Then graph xsp (1) together with (for comparison) the adjusted forcing function F₁ (t)= F(t)/mw. 7. x" + 4x² + 4x = 10 cos 31 8. x+3x+ 5x = -4 cos 5t

In each of Problems 7 through 10, find the steady periodic so- lution xsp (1) = C cos(oot - a) of the given equation mx" + ex' + kx = F(t) with periodic forcing function F(t) of fre- quency o. Then graph xsp (1) together with (for comparison) the adjusted forcing function F₁ (t)= F(t)/mw. 7. x" + 4x² + 4x = 10 cos 31 8. x+3x+ 5x = -4 cos 5t

Advanced Engineering Mathematics
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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In each of Problems 7 through 10, find the steady periodic so- lution Xsp(1) = C cos(@t-a) of the given equation mx" + ex' + kx = F(t) with periodic forcing function F(t) of fre- quency w. Then graph xsp (1) together with (for comparison) the adjusted forcing function F₁ (t) = F(1)/mw. 7. x" + 4x² + 4x = 10 cos 31 8. x" + 3x + 5x = -4 cos 5t 9. 2x" + 2x² + x = 3 sin 101 10. x" + 3x + 3x = 8 cos 10r + 6 sin 101
Transcribed Image Text:In each of Problems 7 through 10, find the steady periodic so- lution Xsp(1) = C cos(@t-a) of the given equation mx" + ex' + kx = F(t) with periodic forcing function F(t) of fre- quency w. Then graph xsp (1) together with (for comparison) the adjusted forcing function F₁ (t) = F(1)/mw. 7. x" + 4x² + 4x = 10 cos 31 8. x" + 3x + 5x = -4 cos 5t 9. 2x" + 2x² + x = 3 sin 101 10. x" + 3x + 3x = 8 cos 10r + 6 sin 101
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