Electric Circuits, Global Edition
Electric Circuits, Global Edition
10th Edition
ISBN: 9781292060545
Author: James W. Nilsson, Susan Riedel
Publisher: Pearson Education Limited
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Chapter 12, Problem 9P
To determine

Show the result L[δ(t)]=1.

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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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