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6.                  Consider the initial value problem                   &

6.                  Consider the initial value problem

                                           y'’ + 2y’ + 2y = δ(t − π);           y(0) = 0, y’(0) = 1.

a.    Find the solution to the initial value problem.

b.    Sketch a plot of the solution for t ∈ [0,3π].

c.    Describe the behavior of the solution. How is this system damped?

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Answer #1

Doubt in this then comment below.. i will help you..

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please thumbs up for this solution...thanks..

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c ) ....

as t increase, solution moves sinosoidal with amplitude decrease exponentially...

and at the end is tends toward 0...

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since solution decrease and also for all value of t is is depend only on particular solution .therefore it is damped system....

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