20 hours ago

my attempt to do the exercises in sicp.

## Tuesday, January 4, 2011

### sicp exercise 3.78

;; Exercise 3.78.

;;Figure 3.35: Signal-flow diagram for the solution to a second-order linear differential equation.

;;Consider the problem of designing a signal-processing system to study the homogeneous second-order linear differential equation

;;The output stream, modeling y, is generated by a network that contains a loop. This is because the value of d2y/dt2 depends upon the values of y and dy/dt and both of these are determined by integrating d2y/dt2. The diagram we would like to encode is shown in figure 3.35. Write a procedure solve-2nd that takes as arguments the constants a, b, and dt and the initial values y0 and dy0 for y and dy/dt and generates the stream of successive values of y.

(define (display-line str)

(display str)

(newline))

(define (display-stream str num)

(define (internal index)

(if (> index num) 'printed

(begin

(display-line (stream-ref str index))

(internal (+ 1 index)))))

(newline)

(internal 0))

(define (scale-stream stream factor)

(stream-map (lambda (x) (* x factor)) stream))

(define (add-streams s1 s2)

(stream-map + s1 s2))

(define (integral delayed-integrand initial-value dt)

(define int

(cons-stream initial-value

(let ((integrand (force delayed-integrand)))

(add-streams (scale-stream integrand dt)

int))))

int)

(define (solve-2nd a b dt y0 dy0)

(define y (integral (delay dy) y0 dt))

(define dy (integral (delay ddy) dy0 dt))

(define ddy (add-streams (scale-stream dy a)

(scale-stream y b)))

y)

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