Concept explainers
Determine the fundamental frequency, fundamental radian frequency, and period of the following: (a) 5 sin 9t; (b) 200 cos 70t; (c) 4 sin(4t − 10°); (d) 4 sin(4t + 10°).
(a)
The fundamental frequency, fundamental angular frequency and period of the given function.
Answer to Problem 1E
The fundamental angular frequency of the given function is
Explanation of Solution
Given data:
The given function
Calculation:
The general form of the function is given as,
Here,
Compare the given function with equation (1).
The fundamental radian frequency is,
The fundamental frequency is given as,
Substitute
The time period is given as,
Substitute
Conclusion:
Therefore, the fundamental angular frequency of the given function is
(b)
The fundamental frequency, fundamental angular frequency and period of the given function
Answer to Problem 1E
The fundamental angular frequency of the given function is
Explanation of Solution
Given data:
The given function
Calculation:
Compare the given function with equation (1).
The fundamental radian frequency is,
Substitute
Substitute
Conclusion:
Therefore, the fundamental angular frequency of the given function is
(c)
The fundamental frequency, fundamental angular frequency and period of the given function
Answer to Problem 1E
The fundamental angular frequency of the given function is
Explanation of Solution
Given data:
The given function
Calculation:
Compare the given function with equation (1).
The fundamental radian frequency is,
Substitute
Substitute
Conclusion:
Therefore, the fundamental angular frequency of the given function is
(d)
The fundamental frequency, fundamental angular frequency and period of the given function
Answer to Problem 1E
The fundamental angular frequency of the given function is
Explanation of Solution
Given data:
The given function
Calculation:
Compare the given function with equation (1).
The fundamental radian frequency is,
Substitute
Substitute
Conclusion:
Therefore, the fundamental angular frequency of the given function is
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