We now wish to illustrate how several op amp circuits can be interconnected to solve a

Chapter 24, Problem 65

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We now wish to illustrate how several op amp circuits can be interconnected to solve a differential equation. a) Derive the differential equation for the springmass system shown in Fig. P8.65(a). Assume that the force exerted by the spring is directly proportional to the spring displacement, thatthe mass is constant, and that the frictionalforce is directly proportional to the velocity ofthe moving mass.b) Rewrite the differential equation derived in (a)so that the highest order derivative is expressedas a function of all the other terms in the equation.Now assume that a voltage equal tois available and by successive integrationsgenerates and x. We can synthesizethe coefficients in the equations by scalingamplifiers, and we can combine the termsrequired to generate by using a summingamplifier. With these ideas in mind, analyzethe interconnection shown in Fig. P8.65(b).In particular, describe the purpose of eachshaded area in the circuit and describe the signalat the points labeled B, C, D, E, and F,assuming the signal at A representsAlso discuss the parameters R;and in terms of the coefficientsin the differential equation.

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