Concept explainers
The Laplace transform of the given periodic function.
Answer to Problem 1P
The Laplace transform of the given periodic function is
Explanation of Solution
Given data:
The given periodic waveform is shown in Figure 1.
The time period of this waveform is
Calculation:
The function expression calculated from the figure is written as,
Here,
The angular frequency is given by,
Substitute
Substitute
The Laplace transform of a periodic signal is written as,
The Laplace transform of the function
Substitute
The general form of
Substitute
Substitute
The above equation is divided into two parts as,
The first part
The second part
Solve for
Solve further as,
Solve further as,
Solve equation (6) for
Solve further as,
Solve further as,
Substitute
The Laplace transform of
Substitute
Substitute
Substitute
Substitute
Conclusion:
Therefore, the Laplace transform of the given periodic function is.
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Chapter A7 Solutions
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