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MAE142_Lecture2

# MAE142_Lecture2 - Transfer Function Review Laplace...

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Transfer Function Review Laplace Transform Transfer Functions Frequency Response MAE 142 Wright R2600 Engine

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2 MAE 142 Laplace Transform The Laplace Transform converts time-domain functions into Laplace Domain functions. The Inverse Laplace Transform converts Laplace functions back to the time domain. L [ f t ]= 0 f t e st dt F s L 1 [ F s ]≡ f t t = time , s = Laplace variable Note that s is a complex number with real and imaginary parts: s = j ℜ s = ℑ s = j = 1
3 MAE 142 Some Simple Time Functions Unit Step Function Rectangular Pulse u t = { 0, t 0 1, t 0 } L [ u t ]= 0 e st dt = 1 s p t = 1 a [ u t − u t a ] lim a 0 P s = 1 L [ p t ]= P s = 1 as [ 1 e as ] t p t a 1 a t u t 1.0 Impulse Function:

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4 MAE 142 Ramp and Trig Functions Ramp Function Trigonometric Functions L [ sin  t ]= s
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MAE142_Lecture2 - Transfer Function Review Laplace...

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