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2. Find the inverse Laplace of the following functions using Convolution Integral. a) Leave your answer in integral form. F(s) (s²+4)² o) Evaluate the convolution integral. F(s) = 1 s² (s² + k²)

2. Find the inverse Laplace of the following functions using Convolution Integral. a) Leave your answer in integral form. F(s) (s²+4)² o) Evaluate the convolution integral. F(s) = 1 s² (s² + k²)

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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Plz do both parts and take a thumb up
2. L(eat f(t)) = F(s-a); L-¹ (F(s-a)) = eªt f(t) where f(t) = [~ ¹(F(s)) c(f(t-c)u (t)) = e "Lif(t)); ¹(e-F(s)) = f(t-c)u(t) where f(t) = £¹ (F(s)) L(8(t-c)) = e-s; L(f(t)-g(t)) = F(s)G(s); f(t).g(t) = L(f(t)8(t-c)) = f(c)e-s L¹(F(s) G(s)) = f(t) g(t) F(s) = Find the inverse Laplace of the following functions using Convolution Integral. a) Leave your answer in integral form. FORMULAS TO REMEMBER (s²+4)² F(s) = D) Evaluate the convolution integral. s² (s²+k²) - [ f(t)g (t = v)dr = [*9( -T)dt = g(t)f(t-1)dr
Transcribed Image Text:2. L(eat f(t)) = F(s-a); L-¹ (F(s-a)) = eªt f(t) where f(t) = [~ ¹(F(s)) c(f(t-c)u (t)) = e "Lif(t)); ¹(e-F(s)) = f(t-c)u(t) where f(t) = £¹ (F(s)) L(8(t-c)) = e-s; L(f(t)-g(t)) = F(s)G(s); f(t).g(t) = L(f(t)8(t-c)) = f(c)e-s L¹(F(s) G(s)) = f(t) g(t) F(s) = Find the inverse Laplace of the following functions using Convolution Integral. a) Leave your answer in integral form. FORMULAS TO REMEMBER (s²+4)² F(s) = D) Evaluate the convolution integral. s² (s²+k²) - [ f(t)g (t = v)dr = [*9( -T)dt = g(t)f(t-1)dr
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