Description
1) Evaluate the following Laplace Transforms using the table in the textbook.
a)
L {t
3 − sinh(2t)}
b)
L {(t − 2)2
e
4t
}
c)
L {sin2
(kt)}
d)
L {x(t)}
where
x(t) =
1 0 ≤ t < 2
2 2 ≤ t < 4 0 t ≥ 4 2) Show that all bounded functions are of exponential order. [A function f(x) is bounded if there exists an M > 0 such that |f(x)| ≤ M for all
x in R.]
3) Evaluate the following inverse Laplace Transforms
a)
L −1
s
2
(s + 1)3
b)
L −1
1
s
2 + 4s + 10
4) Use the Laplace Transform to solve the following initial value problem.
y
00 + 4y = e
−t
, y(0) = 2, y0
(0) = 1