Question

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

Answer #1

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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) =

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

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

Find the Laplace transform of f(t) =
?3e3t

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

Find the LaPlace Transform, L(f(t)), for the given f(t).
1.) f(t) = (3-e2t)2
2.) f(t) = 2t U (t-2)
3.) f(t) = tcos4t

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

a.) Find the Laplace transform of ?(?)=1+?(?−5)⋅(?+9)
b.) Find the Laplace transform of?(?)=?(?−4)⋅?^2
c.) Find the Laplace transform of?(?)=?(?−(3?)/2)⋅sin(?)
d.) Find the Laplace transform of ?(?)=?(?−4)⋅?^(−?)

Use Definition 7.1.1,
DEFINITION 7.1.1 Laplace
Transform
Let f be a function defined for
t ≥ 0.
Then the integralℒ{f(t)} =
∞
e−stf(t) dt
0
is said to be the Laplace transform of
f, provided that the integral converges.
to find
ℒ{f(t)}.
(Write your answer as a function of s.)
f(t) = te8t
ℒ{f(t)} =
(s > 8)

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

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