MATHEMATICS EXAM FOR ELECTRONIC ENGINEERING STUDENTS - CORK INSTITUTE OF TECHNOLOGY, Exams of Electrical Engineering

Download MATHEMATICS EXAM FOR ELECTRONIC ENGINEERING STUDENTS - CORK INSTITUTE OF TECHNOLOGY and more Exams Electrical Engineering in PDF only on Docsity! Cork Institute of Technology Bachelor of Engineering in Electronic Engineering — Award (NFQ — Level 7) Winter 2008 MATH7013 MATHEMATICS FOR ELECTRONIC ENGINEERING TM325 (Time: 2 Hours) Answer any three questions. All questions carry equal marks [each 20 marks]. Maximum available marks is 60. Examiners: Dr. Áine Nı́ Shé The accompanying booklet contains: • Table of Laplace transforms; • Formulae for Fourier Analysis. [P.T.O.] 1 Q1 (a) Find (i) L{t3 + cos 4t} (ii) L { sin2 3t } (iii) L−1 { 10 s5 + s + 6 s2 + 6s + 45 } [8 marks] (b) Consider the second order differential equation d2x dt2 + 5 dx dt + 6x = r(t) given that x(0) = x′(0) = 0 (i) Find the transfer function for the input-output system governed by this differential equation; (ii) Find the steady-state response and the transient response to the input r(t) = 18t. [8 marks] (c) Solve the first order differential equation dx dt + x = e−tt given that x(0) = 1 [4 marks] Q2 (a) Plot a pole-zero map for the system F (s) = (s − 3) (s2 + 25)(s2 − 36)(s2 + 2s + 2) Is this system stable? Explain your answer. [6 marks] (b) Sketch a graph of the function f(t) defined by f(t) = { t 0 ≤ t < 4 4 t ≥ 4 and find its Laplace transform. [6 marks] Parts (c), (d) overleaf 2