ch06_5 - Ch 6.5: Impulse Functions In some applications, it...

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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 ), ( + < <- = = + + 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 ), then I ( ) = 1 (independent of ). +- - = = ) ( ) ( ) ( t t dt t g dt t g I + < <- = otherwise , , ) ( t t t c t g , 2 ) ( ) ( ) ( = = = +- - c dt t g dt t g I t t Unit Impulse Function Suppose the forcing function d ( t ) has the form Then as we have seen, I ( ) = 1. ) = 1....
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ch06_5 - Ch 6.5: Impulse Functions In some applications, it...

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