Use the Fourier transform to find vo (t) in the circuit shown in Fig.V(t).-2-120'2+5 H10 0+

For this circuit we need to calculate Vo(t) Using Fourier transform method. Circuit:-

Answered: Use the Fourier transform to find vo…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Use the Fourier transform to find vo (t) in the circuit shown in Fig.
V(t).
-2
-1
2
0
'
2
+
5 H
10 0
+

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These are the steps I did to get my answer:
1. Apply the Fourier transform to transform the circuit
2. Use voltage division
3. From the figure, find V(w) of the given V(t). In this case V(t) = 2 rect(t/4)
4. Apply the Fourier transform formula to find V(w)
5. Vo(w) = (4sin(2w))/(w(2+jw)). I used partial fractions and got Vo(w) = 54.58(1/(2+jw))
6. Apply the inverse of the Fourier transform. Therefore, my final answer is Vo(t)=(54.58e^-(2t)) u(t) V
Could you please check your answer? The expression you obtained for Vo(t) seems wrong. But I also want to make sure that my answer is correct.

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