Question

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

Answer #1

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 of laplace f(t) = 0 if 0<=t<2,
f(t)=4 if t>=2

Find the Laplace transform F(s) = ℒ{ f (t)} of the function
f (t) = (7 − t) [?(t − 4) − ?(t − 6)].

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) =

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 for the following functions. Show all
work.
(a) u(t-1) - u(t-2)
(b) sin(2t-4)u(t-2)

Find the Inverse Laplace Transform of the following
functions
(a)
F(s) =4/s(s2+2s+2)
(b)
F(s) =8/s2(s2+2)

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

Write the function in terms of unit step functions. Find the
Laplace transform of the given function.
f(t) =
4,
0 ≤ t < 6
−3,
t ≥ 6

Find the Laplace transform of the function.
(a) f(t) = 2H3 (t) -2H4 (t)
(b) f(t) = t2H3 (t)
(c) Solve x'= -x + H1 (t) - H2 (t), x(0) =
1

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