Q. Analog Computers?

Although not used as much as the digital computer (which nowadays forms the basic tool for numerical analysis and the solution of algebraic as well as differential equations), the analog computer still retains some significant advantages over the digital computer. A physical system can be represented by a set of differential equations which can be modeled on an analog computer that uses continuously varying voltages to represent system variables. The differential equation is solved by the computer, whereas the modeled quantities are readily varied by adjusting passive components on the computer. The mathematical functions (integration, addition, scaling, and inversion) are provided by op amps.

The analog computer components are shown in Figure. Let the ordinary differential equation to be solved be

The simulation of the solution is accomplished by the connection diagram of Figure 5.4.19. Time scaling is done by redefining t as t = ατ , in which case the differential equation [Equation] becomes

The coefficients may simply be scaled by the appropriate factors to change the solution time of the analog computer. For example, if α = 20, then t = 20 s corresponds to τ = 1 s, and thus the solution time may be reduced.