Question

Find the Laplace Transformation of the Function

f(t) = t, 0 < t < 1

t^2, 1 < t < 2

0, 2 < t <inf

Answer #1

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

Find the Laplace transform of the given function:
f(t)=(t-3)u2(t)-(t-2)u3(t),
where uc(t) denotes the Heaviside function, which is 0 for
t<c and 1 for t≥c.
Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).
L{f(t)}=
_________________ , s>0

Consider a function (fx) such that L(f)(2) = 1; f(0)=1;
f'(0)=0
Where L(f)(s) denotes the Laplace transform of f(t)
Calculate L(f'')(2)

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

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)

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

Use Laplace transformation to find the convolution product: t^2
* (420t^4 + 60t)

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 inverse laplace transformation of
F(s) = (s-3) / (s^2 - 8s + 17)

Find the Laplace transform of the given function. (Express your
answer in terms of s.)
f(t) =
t
3e−(t − τ) sin τ dτ
0

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