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x2=a*cos(w*t); % x2-array constructed
plot(t,x1,t,x2,'--')

In-Class Exercises
Pb. 3.15 Determine the phase relation between the sine and cosine func-
tions of the same argument.
Pb. 3.16 The meaning of amplitude, angular frequency, and phase can be
better understood using MATLAB to obtain graphs of the cosine function for
a family of a values, ω values, and φ values.
a. With ω = 1 and φ = π/3, plot the cosine curves corresponding to
a = 1:0.1:2.
b. With a = 1 and ω = 1, plot the cosine curves corresponding to
φ = 0:π/10:π.
c. With a = 1 and φ = π/4, plot the cosine curves corresponding to
ω = 1:0.1:2.

Homework Problem
Pb. 3.17 Find the period of the function obtained by summing the following
three cosine functions:

x = cos( t 3 +/ π / 3), x = cos( t + ),π x = 1 cos  3 ( t + )π 
3
1 2 3  
3 2
Verify your result graphically.

3.6 Examples with the Logarithmic Function

3.6.1 Ideal Coaxial Capacitor
An ideal capacitor can be loosely defined as two metallic plates separated by
an insulator. If a potential is established between the plates, for example
through the means of connecting the two plates to the different terminals of
a battery, the plates will be charged by equal and opposite charges, with the
battery serving as a pump to move the charges around. The capacitance of a

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