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Exercises 22-26: Rewrite the function y(t) in the form y(t) = Reat cos(ßt - 8), where 0 ≤ 8 <2n. Use this representation to sketch a graph of the given function, on a domain sufficiently large to display its main features. 22. y(t) = sint + cost 23. y(t) = сos лt - sinлt e cost +Bette

Exercises 22-26: Rewrite the function y(t) in the form y(t) = Reat cos(ßt - 8), where 0 ≤ 8 <2n. Use this representation to sketch a graph of the given function, on a domain sufficiently large to display its main features. 22. y(t) = sint + cost 23. y(t) = сos лt - sinлt e cost +Bette

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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Please show all work and do all parts. Only do question 22.
18. y(t) = √20 19. y(t) = 2e' cos(лt - л), 20. y(t) = e cos(лt - л), 21. y(t) = 3e-2 cos(t-1/2), Exercises 22-26: to = 11 to = 0 to = 0 Rewrite the function y(t) in the form y(t) = Rea cos(ßt - 8), where 0 ≤ 8 < 27. Use this representation to sketch a graph of the given function, on a domain sufficiently large to display its main features. 22. y(t) = sint + cost 24. y(t) = e' cost+√3e¹ sint 26. y(t) = e-2t cos 2t - e-2¹ sin 2t Exercises 27-29: In each exercise, the figure shows the graph of the solution of an initial value problem y"+ay+by = 0, y(0) = yo, y'(0)=yo. Use the information given to express the solu- tion in the form y(t) = R cos(ßt - 8), where 0 ≤ 8 < 2л. Determine the constants a, b.yo and yo. 23. y(t) = cosлt - sinлt 25. y(t) = -e¹ cost +√3e-¹ sint
Transcribed Image Text:18. y(t) = √20 19. y(t) = 2e' cos(лt - л), 20. y(t) = e cos(лt - л), 21. y(t) = 3e-2 cos(t-1/2), Exercises 22-26: to = 11 to = 0 to = 0 Rewrite the function y(t) in the form y(t) = Rea cos(ßt - 8), where 0 ≤ 8 < 27. Use this representation to sketch a graph of the given function, on a domain sufficiently large to display its main features. 22. y(t) = sint + cost 24. y(t) = e' cost+√3e¹ sint 26. y(t) = e-2t cos 2t - e-2¹ sin 2t Exercises 27-29: In each exercise, the figure shows the graph of the solution of an initial value problem y"+ay+by = 0, y(0) = yo, y'(0)=yo. Use the information given to express the solu- tion in the form y(t) = R cos(ßt - 8), where 0 ≤ 8 < 2л. Determine the constants a, b.yo and yo. 23. y(t) = cosлt - sinлt 25. y(t) = -e¹ cost +√3e-¹ sint
Expert Solution
Step 1

Q-22 

y=sin t +cos ty=2 (sint 12+cost 12)y=2 (cost cos π4+ sint sinπ4)y=2  cos(t-π4)y=2  e0t cos(t-π4)

HereR=2α=0β=1δ=π4

 

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