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Unformatted text preview: 1 AE 383 SYSTEM DYNAMICS Lecture Notes 4 (June 27 th 2006) Step and Frequency Response of Ideal Elements We want to know the “dynamic response” of these ideal elements. Dynamic response could refer to response to any time-varying input, but two “standard” inputs are very important; the “step input” and the “sinusoidal input”. The constitutive equation for the spring was: k f x s = When f is a step function x will also be a step function (only for an ideal spring). Step input of magnitude f s and the step response of ideal spring The sinusoidal input is the most important one. It is the bases of the frequency response method. Frequency response : Response of the system when the input is a perfect sine wave. Let f = f sin( ω t) be the input f = amplitude (Newton) ω = frequency (rad/s) or Hertz s rad cycle Hertz π 2 sec 1 = = For an ideal spring element t f k x ω sin 1 = So at every frequency the amplitude ratio of k A A f x 1 f input of Amplitude output x of Amplitude = = time f s time f s /k x s 2...
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