Problem Set 10 (BONUS SET) (1) Find the Laplace transform of each given function (do not forget to show your work, most of these calculations follow by a straightforward calculation, but you may use any of the identities on table 6.2.1 of the textbook or any of the identities given in class) (a) f(t) = te" – t²e¯4 (b) f(t) = 21² + 2t + 4 (2) Find the inverse Laplace transform of the following functions 1 (a) F(s) %3D (s – 2)4 (b) F(s) : s2 + 4s + 5
Problem Set 10 (BONUS SET) (1) Find the Laplace transform of each given function (do not forget to show your work, most of these calculations follow by a straightforward calculation, but you may use any of the identities on table 6.2.1 of the textbook or any of the identities given in class) (a) f(t) = te" – t²e¯4 (b) f(t) = 21² + 2t + 4 (2) Find the inverse Laplace transform of the following functions 1 (a) F(s) %3D (s – 2)4 (b) F(s) : s2 + 4s + 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem Set 10 (BONUS SET)
(1) Find the Laplace transform of each given function (do not forget to show your work,
most of these calculations follow by a straightforward calculation, but you may use
any of the identities on table 6.2.1 of the textbook or any of the identities given in
class)
(a) f(t) = te" – t²e-t
(b) f(t) = 21² + 2t +4
(2) Find the inverse Laplace transform of the following functions
1
(а) F(:) —
(s – 2)4
(b) F(s) =
s2 + 4s + 5
(3) Use Laplace's transform to solve the following initial value problems
(a) ü + 4ủ = 1, u(0) = 1, ủ(0) = 0
(b) й + и%3 sin(?), и(0) — 0, й(0) — 1
(4) (BONUS) Find the inverse Laplace transform of the following functions
7
(a) F(s) =
(s² + 1)(s² + 4)
4s2 – 2s + 6
(b) F(s) =
s(s² + 4)
(5) (BONUS) A function f : R →R is said to be periodic with period T if T is a number
such that f(t+T) = f(t) for all t e R. Show that if f is periodic with period T then
1
L(F(1))(s) =
1-e-sT
Use this to compute the Laplace transform L(f) of the function f given by
S 1, 0<t<1
S(t) = { 0. 1<t< 2,
with f(t+2) = f(t) for all t.
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