Most of these exercises are of an advanced nature. However, any of the exercises from Chap...

Most of these exercises are of an advanced nature. However, any of the exercises from Chapter 8 may be done using odesolve, so look there for more elementary exercises.

Something called a scroll circuit is a double looped circuit with two capacitors, an inductor, and a nonlinear resistor. After scaling, the circuit is described by the following system of equations,

xʹ = −cf(y − x)

yʹ = −f(y − x)−z

zʹ = ky

where

f(v) = −av + 0.5(a + b)(|v + 1| − |v − 1|)

describes the current passing through the nonlinear resistor as a function of the voltage drop across the resistor (after scaling).

a) Enter the equations in odesolve as follows.

xʹ = −c*p

y1 = −p − z

z' = k*y

b) Enter the initial conditions x(0) = y(0) = z(0) = 1 and the parameters a = 0.07, b = 0.1, c = 0.1, and k = 1.

c) Enter the following in an expression edit field.

p = −a*(y − x) + 0.5*(a + b)*(abs(y − x + 1) − abs(y − x − 1))

d) Set the relative tolerance to le-6. Obtain plots of the solution in xyz-space and the projection on the «-plane. Repeat the experiment for c = 33.