plotXpose is a companion app with the book Mathematics for Electrical Engineering and Computing by Mary Attenborough - click for more info
 

Partially square - Solution

The first 9 terms of the Fourier series are:

(2/pi)*sin(pi*t)+(2/(3*pi))*sin(3*pi*t)+(2/(5*pi))*sin(5*pi*t)+(2/(7*pi))*sin(7*pi*t)+(2/(9*pi))*sin(9*pi*t)


Plot of the partial sum of the first 9 terms of the Fourier Series for a square wave of amplitude 0.5



Plot of the partial sum of the first 9 terms of the Fourier Series for a square wave of amplitude 0.5. (2/pi)*sin(pi*t)+(2/(3*pi))*sin(3*pi*t)+(2/(5*pi))*sin(5*pi*t)+(2/(7*pi))*sin(7*pi*t)+(2/(9*pi))*sin(9*pi*t)


Percentage Overshoot


To find the percentage overshoot near the jump discontinuity we note that the first peak appears to occur at t=0.1.

Tap the Mode icon and the Mode pop-up menu appears - tap Display Position. A double tap on the plot allows input of the t value, giving the following result.

Values for (2/pi)*sin(pi*t)+(2/(3*pi))*sin(3*pi*t)+(2/(5*pi))*sin(5*pi*t)+(2/(7*pi))*sin(7*pi*t)+(2/(9*pi))*sin(9*pi*t):

Function: (0.1, 0.591164)

The percentage overshoot is approximately ((0.590027-0.5) /0.5) * 100 % = approximately 18%.


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plotXpose app is a companion to the book Mathematics for Electrical Engineering and Computing by Mary Attenborough, published by Newnes, 2003.