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(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.

(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.

Advanced Engineering Mathematics
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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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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