7 - Heaviside practice with inverse Laplace transform Heaviside formula: L[ua(t)f(t = a)] = easF(s)Find the inverse transform function for10 F(s) = e^(-28)  e^(-8) 5 = 3√5 1 f(t) 10ua(t) - e^(-8t) 8ua(t) - e^(ft g)
7 - Heaviside practice with inverse Laplace transform Heaviside formula: L[ua(t)f(t = a)] = easF(s)Find the inverse transform function for10 F(s) = e^(-28)  e^(-8) 5 = 3√5 1 f(t)
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SOLVED: Take the Laplace transform of the following initial value and solve for Y(s) = Ly(t): y" ly = sin(t) , 0 < t < 1, sin y(0) = 0, y'(0) = 0, 1 < t < Y(s). Hint: write the right hand side in terms of the Heaviside function. Now find the inverse transform to find y(t) (Use step(t-c) for u(t-c).) Note: (8^2 7^2)(8^2 1) t^2 - 1 (7^4 - 7 3)
SOLVED: Take the Laplace transform of the following initial value and solve for Y(s) = Ly(t): y" ly = sin(t) , 0 < t < 1, sin y(0) = 0, y'(0) = 0, 1 < t < Y(s). Hint: write the right hand side in terms of the Heaviside function. Now find the inverse transform to find y(t) (Use step(t-c) for u(t-c).) Note: (8^2 7^2)(8^2 1) t^2 - 1 (7^4 - 7 3)
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PPT - Lecture 14: Laplace Transform Properties PowerPoint Presentation - ID:226334
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