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Unformatted text preview: Ch 6.5: Impulse Functions In some applications, it is necessary to deal with phenomena of an impulsive nature. For example, an electrical circuit or mechanical system subject to a sudden voltage or force g ( t ) of large magnitude that acts over a short time interval about t . The differential equation will then have the form small. is and otherwise , , big ) ( where ), ( + < < = = + ′ + ′ ′ τ τ τ t t t t g t g cy y b y a Measuring Impulse In a mechanical system, where g ( t ) is a force, the total impulse of this force is measured by the integral Note that if g ( t ) has the form then In particular, if c = 1/(2 τ ), then I ( τ ) = 1 (independent of τ ). ∫ ∫ + ∞ ∞ = = τ τ τ ) ( ) ( ) ( t t dt t g dt t g I + < < = otherwise , , ) ( τ τ t t t c t g , 2 ) ( ) ( ) ( = = = ∫ ∫ + ∞ ∞ τ τ τ τ τ c dt t g dt t g I t t Unit Impulse Function Suppose the forcing function d τ ( t ) has the form Then as we have seen, I ( τ ) = 1. ) = 1....
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This note was uploaded on 08/13/2009 for the course DIFF 2343632 taught by Professor Csar during the Fall '09 term at Middle East Technical University.
 Fall '09
 Csar

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