Use the Laplace transform to find the solution of y"+Ay'+25 y=e¯sint for y'(0)=y(0)=1 & A=6. Then, determine the largest value of A so that y(t) is a decaying sinusoidal function, ie. y exhibits...

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Extracted text: Use the Laplace transform to find the solution of y"+Ay'+25 y=e¯sint for y'(0)=y(0)=1 & A=6. Then, determine the largest value of A so that y(t) is a decaying sinusoidal function, ie. y exhibits oscillation but its amplitude approaches zero as 2. t → ∞.