Question

Derive the Laplace transform for the following time

functions:

a. sin ωt u(t)

b. cos ωt u(t)

Answer #1

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)

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:
1. e^(-2t+1)
2. cos^2(2t)
3. sin^2(3t)

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 sin root t and hence deduce cos
root t all over root t

Use time-shift property to find the Laplace-image of
a.)sin(t-b) *1(t-b)
b.) cos^2(t-b)*1(t-b)

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

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 f(t) = 2t U (t – 2)

Laplace transform,using shift on t-axis theorem of
(t-2a)* u(t-a)

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