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# plugin-math245lab11 - Math245 Computer Lab set#11 Spring...

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Unformatted text preview: Math245 Computer Lab set #11, Spring 2009 System Response to Impulse Forcing The impulse forcing function( δ-function) is an unbounded function(i.e., δ ( t ) → ∞ as t → 0). Numerical simulations of ODEs that contain the impulse forcing functions are, in general, impossible because com- puters are incapable of handling the unbounded number or even finite but large numbers(e.g., > 10 308 ). In practical engineering applications, however, such impulse forcing functions are bounded. For instance a strength of the impulsive electrical excitation to an electrical circuit is always finite because the maximum power of the exciter is physically limited. Also, unlike the δ-function the duration of such an excitation is always finite, not identically zero. Numerical simulations of the impulsively forced systems, therefore, can be performed employing finite impulse forcing functions imposed during a short time interval. Example We consider, as an example, the linear forced-oscillator problem written as y 00 + y = f k ( t ) , y (0) = y (0) = 0 , (1) where f k ( t ) is an integral-unit pulse forcing function centered at t = 4 whose width is 2 k and whose height is 1 / 2 k as given by f k ( t ) = 1 2 k { u ( t- (4- k ))- u ( t- (4 + k )) } . (2) 1 2 k f k 4 4- k 4 + k ......................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..............................................
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plugin-math245lab11 - Math245 Computer Lab set#11 Spring...

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