Question

Find the Laplace transform of the following functions:

1. (4t^{3}+9t^{2})/t

2. (10+2t)^{2}

3. 5e^{7t-2}

4. -3t^{4}e^{5t}

5. 2sqrt(t) +7t

6. 10t^{3/2}
-e^{-10t}

Answer #1

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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:
(t^3 - 3t +2)e^(-2t)

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

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)

Determine the Laplace transform of the following functions.
δ(t)H(t − 2) + δ(t − 3)H(t)
answer :1+e^-3s
y '' + 3y' + 2y = (2t + 1)H(t − 3), y(0) = 1, y ' (0) = 2
answer
y(t) = 4e^ −t − 3e ^−2t + (3e −2t+6 − 5e −t+3 + t − 1)H(t −
3)

Given the following Laplace transform functions and input
wave-forms, find the output signal.
G(s)=(s^2+3s+4)/s(s+1),v in(t)=3sin(2t-0.15)

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

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

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) =

Use properties of the Laplace transform to solve for the
transform of the following functions of t.
(a) (10 points) (t^2) +( e^t) (sint)
(b) (10 points) 2(t^2)(e^−1) − t + cos4t

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