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In Exercises 7-10, place each equation in the form y Ae-t cos(at). Then, on one plot, place the graphs of y = Ae cos(wt - ), y = Aect, and y -Ae-ct. For the last two, use a different line style and/or color than for the first. == 8. y = e-¹/4 (√3 cos 4t - sin 4t)

In Exercises 7-10, place each equation in the form y Ae-t cos(at). Then, on one plot, place the graphs of y = Ae cos(wt - ), y = Aect, and y -Ae-ct. For the last two, use a different line style and/or color than for the first. == 8. y = e-¹/4 (√3 cos 4t - sin 4t)

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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4.48" In Exercises 7-10, place each equation in the form y Ae-ct cos(wt ). Then, on one plot, place the graphs of y = Ae* cos(wt - o), y = Ae-t, and y = -Ae-t. For the last two, use a different line style and/or color than for the first. 8. y = e-¹/4 (√3 cos 4t - sin 4t)
Transcribed Image Text:4.48" In Exercises 7-10, place each equation in the form y Ae-ct cos(wt ). Then, on one plot, place the graphs of y = Ae* cos(wt - o), y = Ae-t, and y = -Ae-t. For the last two, use a different line style and/or color than for the first. 8. y = e-¹/4 (√3 cos 4t - sin 4t)
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According to question we have y=e-t4(3cos 4t-sin 4t)Now,3cos 4t-sin 4t = 2(32cos 4t-12sin 4t)=2(cosπ6cos 4t-sinπ612sin 4t)=2cos(4t+π6)Hence we have y=2e-t4cos(4t+π6)

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