Use the Laplace transform to find the solution of y"+8 y'+Ay=e¯'sint for y'(0)=y(0)=1 & A=25. Then, determine the largest value of A so that y(t) is a decaying sinusoidal function, ie. y exhibits...

Extracted text: Use the Laplace transform to find the solution of y"+8 y'+Ay=e¯'sint for y'(0)=y(0)=1 & A=25. 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 t - 00.