Question

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)

Answer #1

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

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

Compute Laplace transform of the following functions.
(Please show all the steps)
f)v(t)=(17e^(-4t)-14e^(-5t))u(t)V
g)v(t)=10e^(-5t)(cos(4t+36.86(degrees))(u(t))

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

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)

Use the Laplace Transform to construct a second-order linear
differential equation for the following function:
f(t) = u(t−π)e(5t)sin(2t)
where u(t) is the Heaviside unit step function.

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 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

Consider the differential equation y”+5y’+6y=f(t). Write the
form of the particular solution if f(t) is the following. Do not
solve.
(a) f(t)= 5t*e^(-2t)
(b) f(t)= t^2*sin(2t)
(c) f(t)= t + 1
(d) f(t)= 2t^2*e^(-3t)
(e) f(t)= 4t^2+3t

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