Question

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

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)

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

Find the Laplace transform of the following functions.
(a) f (t) = { 7 0 < t ≤ 4 8 t ≥ 4
(b) f (t) = { t2 0 ≤ t < 2 0 t ≥ 2
(c) f (t) = { 0 0 ≤ t < π/9 cos[7(t − π/9)] t ≥
π/9

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)

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

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

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)

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

Find the Laplace transform of:
(t^3 - 3t +2)e^(-2t)

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