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Using only the Laplace transform table (I obtain the Laplace transform of the following function: f(t) = cosh(6t) + 8t² + t,

Using only the Laplace transform table (I obtain the Laplace transform of the following function: f(t) = cosh(6t) + 8t² + t,

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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Laplace transform question, substitution for cosh is given

(a) f(t) (b) C₂ t ekt ca constant na positive integer k a constant sin at, cos at, a a real constant a a real constant esin at, k and a real constants e-*t cos at, k and a real constants L{f(t)} = F(s) C L{tf(t)} = (-1)"- S - = - dºF(s) ds" s- k a s² + a² S ² + a² a (s + k)² + a² s+k (s + k)² + a² Linearity: First shift theorem: L{ef(t)} = F(sa), Derivative of transform: Region of convergence Re(s) > 0 Re(s) > 0 Re(s) > 0 Re(s) > Re(K) Re(s) > 0 Re(s) > 0 L{f(t)} = F(s), Re(s) > 0₁ and L{g(t)} = G(s), Re(s) > 0₂ L{af(t) + ßg(t)} = aF(s) + BG(s), Re(s) > max(₁, ₂) Re(s) > ₁ + Re(a) Re(s) > -k Re(s) > -k (n= 1, 2, ...), Re(s) > 0₁
Transcribed Image Text:(a) f(t) (b) C₂ t ekt ca constant na positive integer k a constant sin at, cos at, a a real constant a a real constant esin at, k and a real constants e-*t cos at, k and a real constants L{f(t)} = F(s) C L{tf(t)} = (-1)"- S - = - dºF(s) ds" s- k a s² + a² S ² + a² a (s + k)² + a² s+k (s + k)² + a² Linearity: First shift theorem: L{ef(t)} = F(sa), Derivative of transform: Region of convergence Re(s) > 0 Re(s) > 0 Re(s) > 0 Re(s) > Re(K) Re(s) > 0 Re(s) > 0 L{f(t)} = F(s), Re(s) > 0₁ and L{g(t)} = G(s), Re(s) > 0₂ L{af(t) + ßg(t)} = aF(s) + BG(s), Re(s) > max(₁, ₂) Re(s) > ₁ + Re(a) Re(s) > -k Re(s) > -k (n= 1, 2, ...), Re(s) > 0₁
Using only the Laplace transform table (Figure 11.5) in the Glyn James textbook, obtain the Laplace transform of the following function: f(t) = cosh(6t) + 8t² + t, e te- where "cosh" stands for hyperbolic cosine and cosh(x) = ²42-²
Transcribed Image Text:Using only the Laplace transform table (Figure 11.5) in the Glyn James textbook, obtain the Laplace transform of the following function: f(t) = cosh(6t) + 8t² + t, e te- where "cosh" stands for hyperbolic cosine and cosh(x) = ²42-²
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