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

Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: sin(π ) , 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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Need help with this cal-4 question I got...

(1/(pi^2-9))((sin(3t)/3)-sin(pit)/pi)-((sin(3(t-1))/3)-(sin(pi(t-1))/pi))step(t-1)

but that was in correct.

Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: sin(π ) , 0<t<1 0, y" + 9y = 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) (1/(pi^2-9)((sin(3t)/3)-sin(pit)/pi)-((sin(3(t-1))/3)-(sin . (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)}: sin(π ) , 0<t<1 0, y" + 9y = 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) (1/(pi^2-9)((sin(3t)/3)-sin(pit)/pi)-((sin(3(t-1))/3)-(sin . (Use step(t-c) for uc(t) .) Note: 1 1 (s2 + 7²)(s² + 9) 9 s² + 9 s2 + 72
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
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