POWER SYSTEM ANALYSIS+DESIGN-EBK >I<
6th Edition
ISBN: 9781337259170
Author: Glover
Publisher: INTER CENG
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Suppose the Laplace transform of a causal signal x₁ (t) is given by
X₁(s)
s+2
s²+1
(a) What is the Fourier transform X₁ (w) of the signal?
(b) Using the Laplace transform properties, find the Laplace transform of the following signal
x2(t).
x2(t) = e³ x₁(t−1)-4x₁(4)
Note, you do not need to simplify the expression of X2(s). However, state whether it is
possible to write X2(s) as a rational fraction (i.e. ratio of polynomials) in s.
Consider the following mechanical system. In the figure, y(t) denotes the displacement of the
mass from its equilibrium position and u(t) denotes the force applied to the mass.
k1
kz
- y(t)
-0000
0000
3
► u(t)
b
a) Find the differential equation model of the system.
b) Find the state-space model for the system. Write x, A, B, C and D clearly in your answer.
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