Question

Compute the Laplace transform of functions

a) f(t) = e^(−3t) sin(5t)

b) f(t) = (2t + 3)e^(−t)

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)

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

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))

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.

Use the Laplace transform to solve the given integral equation.
f(t) = 2t − 4 t 0 sin(τ) f(t − τ) dτ

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

Use the definition of the Laplace transform to find the
transform of:
f(t)= at+ b cos(2t), where a, b are real numbers.
Please solve using simple and easy to follow steps (here for
learning not for answers)
Thanks

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)

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