Question

Laplace transform,using shift on t-axis theorem of

(t-2a)* u(t-a)

Answer #1

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

Find the inverse Laplace transform of the function by using the
convolution theorem.
F(s) =
1
(s + 4)2(s2 + 4)
ℒ−1{F(s)}(t) =
t
0
dτ

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)

Find the Laplace transform of
f(t)=sinh(at)
f(t)=u(sub2)(t)t+1)
f(t)=t^2δ(t-3)

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 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))

Determine y(t) using the inverse Laplace transform method for
dynamic systems
y"(t) + 9y(t) = e^t
y(0)= -2
y'(0)= 5

Solve y'-3y=2e^t y(0)=e^3-e using Laplace transform.

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.

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