ENEE 241 02*
HOMEWORK ASSIGNMENT 3
Due Wed 02/06
Use your calculator for algebraic and trigonometric functions only, as indicated. Trialanderror
or graphical solutions to parts (i)–(iii) are not acceptable.
Consider the sinusoid
x
(
t
) =
A
cos(Ω
t
+
φ
), where
A >
0 and
φ
∈
(

π,π
]. Time
t
is in seconds.
(i) (6 pts.)
If it is known that
x
(0) =
x
(0
.
160) =
x
(0
.
180) = 2
.
5
and that
x
(
t
)
6
= 2
.
5 for all other times
t
between 0 and 0.180, determine: the period
T
(in seconds),
angular frequency Ω (in rad/sec) and cyclic frequency
f
(in Hz).
No trigonometric functions are
needed for this part.
(ii) (5 pts.)
What is the value of
φ
in radians?
Again, no trigonometric functions are needed for
this part.
(iii) (5 pts.)
Having determined Ω and
φ
, use the cosine function on your calculator to determine
A
.
(iv) (4 pts.)
Write simple MATLAB code which computes and plots two periods of
x
(
t
) starting
at
t
= 0, using 150 uniformly spaced samples per period (i.e., a total of 300 samples). Attach a
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 Spring '08
 staff
 Trigonometry, Periodic function, Euler's formula

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