1. The Laplace transform of a function f(t) is given by the expression F(e) = L{S(} = [S(}»"dt Find the Laplace transform of the following functions: f(t) = t(e-2t + sin at) f(t) = e¬3t cos(2wt) cos(3wt) f(7t – 10) а. b. c.

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1. The Laplace transform of a function f(t) is given by the expression
F(s)= L{f(} = [S(@}*dt
Find the Laplace transform of the following functions:
f (t) = t(e¬2t + sin at)
f(t) = e-3t cos(2wt) cos(3wt)
ƒ(7t – 10)
а.
b.
с.
Find the inverse Laplace transform of the following functions:
1
d.
F(s) =
s²(s²+16)
cs+d-2c
-4s
(s2 +6s+10)
s² +10s+8
F (s) =
е.
f.
F(s) =
s² +11s+9
g.
* + 3x + 6x = 0, x(0) = 0, x(0) = 3, x(t) =?
Transcribed Image Text:1. The Laplace transform of a function f(t) is given by the expression F(s)= L{f(} = [S(@}*dt Find the Laplace transform of the following functions: f (t) = t(e¬2t + sin at) f(t) = e-3t cos(2wt) cos(3wt) ƒ(7t – 10) а. b. с. Find the inverse Laplace transform of the following functions: 1 d. F(s) = s²(s²+16) cs+d-2c -4s (s2 +6s+10) s² +10s+8 F (s) = е. f. F(s) = s² +11s+9 g. * + 3x + 6x = 0, x(0) = 0, x(0) = 3, x(t) =?
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