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Example text

All other coefficients in the equation were taken fully arbi­ trarily. They can be linear or nonlinear, constant or time varying. Nor were theoretical restrictions put on the order of the differential equation. 41 by dividing by an, there are impor­ tant cases where it is very inconvenient to do so. There are no difficulties involved in setting up analog networks for an ¥= 1 if differentiators are permitted. Since the use of differentiators entails serious noise problems, however, a general procedure is required to synthesize such analog net­ works using only integrators.

G. Equation 3. 7a represents represents its Laplace is the transformed network for the study Initial conditions are taken to be zero. G 1 sC r e c e0(s) e;(s) d (b) f 1 sc c (c) Fig. 7 (a) Integrator with (c) Transformed network. leakage conductance. d (b) s-domain network. J(s) = eo(s), since the voltage between the input grid and ground is approximately zero. 43) The sensitivity coefficients can also be determined using purely experi­ mental methods. 44) This expression is obtained by studying the parameter influences of t:i.

The following is a simple illustration of his method. Example 1. Given the system of differential equations x<2 l + 2x<1> + 3x - y<2l = 0 x<1> + 4y<2> - 3y + y = 0 let x<1l = z y<2) = v so that z - v = 0 In matrix form the s ys tem is represented as z v x y s + 2 -s 3 0 0 0 I 0 I 4s - 3 -1 0 s 0 0 0 -1 0 s 0 26 High· Speed Analog Computers Multiplying the first row by 4 and adding row 2 to it, a matrix suitable for machine programming results in z v 4s + 9 - 3 x y 12 1 0 1 4s - 3 0 1 0 -1 0 s 0 0 0 -1 0 s 0 x(O) y(O) Evidently it is necessary to select suitable scale factors in advance.

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Action of Radiation and Perturbations on Atoms by Slater J.C.

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