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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 10

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online