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Take the Laplace transform of the following initial value and solve for Y(s) = = L{y(t)}: S sin(nt), 0

Take the Laplace transform of the following initial value and solve for Y(s) = = L{y(t)}: S sin(nt), 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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HW9 #8 y"+y={sinlTE) %3D o therwise y both sides g? L-s(0)-O + L= (1+es) $ T %3D + TT? (s*+1) L= (Ite=)T %3D regulor 1 second deley sHint r %3D 1+,5 Pequlat (sinlt) - F (sin(t-1) (1-72H + sin (T(E-)) ) • HCE-) 1 secoad delay
Transcribed Image Text:HW9 #8 y"+y={sinlTE) %3D o therwise y both sides g? L-s(0)-O + L= (1+es) $ T %3D + TT? (s*+1) L= (Ite=)T %3D regulor 1 second deley sHint r %3D 1+,5 Pequlat (sinlt) - F (sin(t-1) (1-72H + sin (T(E-)) ) • HCE-) 1 secoad delay
Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: S sin(at), 0<t<1 y" + 9y = 0, y(0) = 0, y'(0) = 0 1<t Y(s) = (1+e^(-s))pi/((s^2+9)(s^2+pi^2)) . Hint: write the right hand side in terms of the Heaviside function. Now find the inverse transform to find y(t) pi/(pi^2-9)(sin(9t)-(1/pi) sin(pi/t))-(pi/(pi^2-9)(sin(t-9) (Use step(t-c) for uc(t) .) Note: 1 1 (s2 + 7²)(s² + 9) 9 s2 + 9 s2 + 72
Transcribed Image Text:Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: S sin(at), 0<t<1 y" + 9y = 0, y(0) = 0, y'(0) = 0 1<t Y(s) = (1+e^(-s))pi/((s^2+9)(s^2+pi^2)) . Hint: write the right hand side in terms of the Heaviside function. Now find the inverse transform to find y(t) pi/(pi^2-9)(sin(9t)-(1/pi) sin(pi/t))-(pi/(pi^2-9)(sin(t-9) (Use step(t-c) for uc(t) .) Note: 1 1 (s2 + 7²)(s² + 9) 9 s2 + 9 s2 + 72
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