Question

Find the Laplace transform for the following functions. Show all work.

(a) u(t-1) - u(t-2)

(b) sin(2t-4)u(t-2)

Answer #1

Derive the Laplace transform of the following time domain
functions
A) 12 B) 3t sin(5t) u(t) C) 2t^2 cos(3t) u(t) D) 2e^-5t
sin(5t)
E) 8e^-3t cos(4t) F) (cost)&(t-pi/4)

Derive the Laplace transform for the following time
functions:
a. sin ωt u(t)
b. cos ωt u(t)

find the laplace transform f(t) = 2t U (t – 2)

Find the Laplace Transform of the following functions:
1. e^(-2t+1)
2. cos^2(2t)
3. sin^2(3t)

Find the Laplace transform of the following functions:
1. (4t3+9t2)/t
2. (10+2t)2
3. 5e7t-2
4. -3t4e5t
5. 2sqrt(t) +7t
6. 10t3/2
-e-10t

Compute the Laplace transform of functions
a) f(t) = e^(−3t) sin(5t)
b) f(t) = (2t + 3)e^(−t)

a.) Find the Laplace transform of ?(?)=1+?(?−5)⋅(?+9)
b.) Find the Laplace transform of?(?)=?(?−4)⋅?^2
c.) Find the Laplace transform of?(?)=?(?−(3?)/2)⋅sin(?)
d.) Find the Laplace transform of ?(?)=?(?−4)⋅?^(−?)

determine the Laplace transform of the following functions:
a) f(t) = { 1 if 0 < t < 5,
0 if 5 < t < 10,
e^ 4t if t > 10
b) g(t) = 6e −3t − t 2 + 2t − 8

1. Find the Laplace transform of
a.) f(t)=u(t−4)⋅e^t
F(s)=
2. Find the inverse Laplace transform of
a.) F(s)=2e^(−3s)−e^(−2s)−3e^(−6s)−e^(−9s)/s
f(t) =
b.) F(s)=e^(−6s)/s^2−3s−10
f(t) =
c.) F(s)=4e^(−9s)/s^2+16
f(t) =

Find the Laplace transform for the following.
(a.) -42(e^(t-4))U(t-4)
(b.) f(t) = {t, 0≤t<1; 0, 1≤t<2} and f(t)=f(t-2) if
t≥2

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