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Microsoft Word - MLS.Impulse.Response: Author: Bautsch: Software used: Acrobat PDFMaker 7.0.5 for Word: Conversion program: Acrobat Distiller 7.0.5 (Windows) Encrypted: no: Page size: 612 x 792 pts (letter) Version of PDF format: 1.4
More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).
The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram metre per second (kg⋅m/s). The corresponding English engineering unit is the pound-second (lbf⋅s), and in the British Gravitational System, the unit is the slug-foot per second (slug⋅ft/s).
The impulse response can be computed to any desired degree of accuracy by choosing a suitable approximation for δ, and once it is known, it characterizes the system completely. See LTI system theory § Impulse response and convolution. The inverse Fourier transform of the tempered distribution f(ξ) = 1 is the delta function.
If a system initially rests at its equilibrium position, from where it is acted upon by a unit-impulse at the instance t=0, i.e., p(t) in the equation above is a Dirac delta function δ(t), () = | = =, then by solving the differential equation one can get a fundamental solution (known as a unit-impulse response function)
An example response of system to sine wave forcing function. Time axis in units of the time constant τ. The response damps out to become a simple sine wave. Frequency response of system vs. frequency in units of the bandwidth f 3dB. The response is normalized to a zero frequency value of unity, and drops to 1/√2 at the bandwidth.
The unit g (or g) represents multiples of the standard acceleration of gravity and is conventionally used. A shock pulse can be characterised by its peak acceleration, the duration, and the shape of the shock pulse (half sine, triangular, trapezoidal, etc.). The shock response spectrum is a method for further evaluating a mechanical shock. [1]
If the response is measured at point B in direction x (for example), for an excitation at point A in direction y, then the transfer function (crudely Bx/Ay in the frequency domain) is identical to that which is obtained when the response at Ay is measured when excited at Bx. That is Bx/Ay=Ay/Bx. Again this assumes (and is a good test for ...