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3. A particle is subjected to an impulsive force that acts over the timescale-T < t

3. A particle is subjected to an impulsive force that acts over the timescale-T < t

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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3. A particle is subjected to an impulsive force that acts over the timescale-T < t <T and is zero otherwise. It rises, and then declines, linearly with time according to F(t) = Fo [ Po (1 + 1/1) | Fo (1-2) -T<t≤0 0≤t≤T where Fo is a constant. Show that the Fourier transform of this force is, 1 F (W) = √ √ Lx √ √ F(t)e-ist dt √2π and express A in terms of Fo Sketch | F(t) against t, and |Â (w)|2 against w sin² (wT/2) = A- w²T Explain how the features of these diagrams are related to each other and describe what happens as T → 0
Transcribed Image Text:3. A particle is subjected to an impulsive force that acts over the timescale-T < t <T and is zero otherwise. It rises, and then declines, linearly with time according to F(t) = Fo [ Po (1 + 1/1) | Fo (1-2) -T<t≤0 0≤t≤T where Fo is a constant. Show that the Fourier transform of this force is, 1 F (W) = √ √ Lx √ √ F(t)e-ist dt √2π and express A in terms of Fo Sketch | F(t) against t, and |Â (w)|2 against w sin² (wT/2) = A- w²T Explain how the features of these diagrams are related to each other and describe what happens as T → 0
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