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)

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)

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)

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

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)

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