Question

Section 6.4 Discontinuous Forcing Functions: Problem 1 Previous Problem Problem List Next Problem Results for this submission Entered Answer Preview Result 5-5 exp(-28) +4s s2 +64 [55"exp(-2%)+4*S)/[(s*2)-64] incorrect The answer above is NOT correct. (1 point) Consider the following initial value problem: 5, 0t2 (0)4, (0) 0 0, t> 2 Using Y for the Laplace transform of y(t), ie., Y- Ly(t). find the equation you get by taking the Laplace transform of the differential equation and solve for 8 (5-5exp(-2s)+4s/(S 2+64)

Answer 1

"Y^"" + 64y = {5, 0 lessthanorequalto t lessthanorequalto 2 0, t > 2, y(0) = 4, y^;(0) = 0 Apply Laplace, we get L(Y^"" + 64y) = L(Y^"") + 64 L(y) = integral^2_0 e^-st 5 dt + integral^infinity_2 e^-5t, 0 dt because by definition of Laplace S^2 y - sy(0) - y^'(0) + 64y = 5 e^-st/-s