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Problem 3. Find the inverse transform f(t) of F(s) = πT² s² + π² * Use the second shifting theorem(time shifting) : e-38 (s + 2)² If f(t) has the transform F(s), then the "shifted function" if t a has the transform e-a8F(s). That is, if Lf(t) = F(s), then -08 Lf(ta)u(ta) = e-ªs F(s). ƒ(t) = f(t − a)u(t − a) = =

Problem 3. Find the inverse transform f(t) of F(s) = πT² s² + π² * Use the second shifting theorem(time shifting) : e-38 (s + 2)² If f(t) has the transform F(s), then the "shifted function" if t a has the transform e-a8F(s). That is, if Lf(t) = F(s), then -08 Lf(ta)u(ta) = e-ªs F(s). ƒ(t) = f(t − a)u(t − a) = =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 3. Find the inverse transform f(t) of F(s) = πT² s² + π² * Use the second shifting theorem(time shifting) : e-38 (s + 2)² If f(t) has the transform F(s), then the "shifted function" if t <a f(t - a) if t>a has the transform e-a8F(s). That is, if Lf(t) = F(s), then -08 Lf(ta)u(ta) = e-ªs F(s). ƒ(t) = f(t − a)u(t − a) = =
Transcribed Image Text:Problem 3. Find the inverse transform f(t) of F(s) = πT² s² + π² * Use the second shifting theorem(time shifting) : e-38 (s + 2)² If f(t) has the transform F(s), then the "shifted function" if t <a f(t - a) if t>a has the transform e-a8F(s). That is, if Lf(t) = F(s), then -08 Lf(ta)u(ta) = e-ªs F(s). ƒ(t) = f(t − a)u(t − a) = =
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