(a) A signal applied to a servomechanism system is defined by the function as, 0 4 5 f(t) = 2t+1 9 (i) Sketch the function (ii) From the signal you have sketched, discuss the limitation of using step function to represent some practical signal.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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Question 3
(a) A signal applied to a servomechanism system is defined by the function as,
f(t) =
=
5
2t+1
9
0<t≤2
2<t≤4
t> 4
(i) Sketch the function
(ii) From the signal you have sketched, discuss the limitation of using step
function to represent some practical signal.
(iii) Show that f(t) = 5u(t)+2(t − 2)U (t− 2) – 2(t –4)U (t – 4)
where U(t-2) and U(t−4) are unit step functions.
(iv) Hence, determine the Laplace transform of function f(t), i.e. L{f(t)}.
Transcribed Image Text:Question 3 (a) A signal applied to a servomechanism system is defined by the function as, f(t) = = 5 2t+1 9 0<t≤2 2<t≤4 t> 4 (i) Sketch the function (ii) From the signal you have sketched, discuss the limitation of using step function to represent some practical signal. (iii) Show that f(t) = 5u(t)+2(t − 2)U (t− 2) – 2(t –4)U (t – 4) where U(t-2) and U(t−4) are unit step functions. (iv) Hence, determine the Laplace transform of function f(t), i.e. L{f(t)}.
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