Plot the following waveform versus time showing one clear. Complete cycle. Then determine the derivative of the waveform using Eq. (14.1) and sketch one complete cycle of the derivative directly under the Original waveform. Compare the magnitude of the derivative at various points versus the slope of the original sinusoidal function.
To plot:
The graph of the waveform versus time for one complete cycle. Calculate the derivative of the waveform and then draw one complete cycle of it. Also, compare the magnitude of the derivative at various points versus the slope of the original sinusoidal function.
Explanation of Solution
Given:
The given equation is
Calculation:
Let us consider the sinusoidal expression of voltage as:
Standard sinusoidal equation is:
Comparing, we get
Value of frequency will be
Voltage at
Voltage at
Voltage at
Voltage at
Voltage at
Voltage at
Graph showing voltage versus time
Derivative of standard sinusoidal equation is
Value of derivative of voltage at
Value of derivative of voltage at
Value of derivative of voltage at
Value of derivative of voltage at
Value of derivative of voltage at
Value of derivative of voltage at
Graph of derivative of voltage directly under the original waveform:
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