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)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b2b9d69-854a-4c26-a639-4c378ed4e00f%2Fc9866d22-58ab-4a5a-a484-9e2a7cbb22bd%2F2w4o7b7_processed.jpeg&w=3840&q=75)
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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