Problem 21-3    Source:   Problem elaborated by the author of the site.

Sketch the waveform of the function defined as

Solution of the Problem 21-3

In the picture to the side we see the representation of the waveforms according to the f(t) of the problem statement. The first part of f(t) is a step function (illustrated in red color) with amplitude 2 volts and time shifted in 1 s.

The second part (illustrated in orange) is a ramp function with increasing amplitude and time shifted in t = 3 s.

The third part (illustrated in purple) is also a function ramp, but with decreasing amplitude and time shifted in t = 4 s. Note that in t = 4 s, we have two ramp functions (the orange and the purple), one increasing and one decreasing.

This gives a constant voltage between the times 4 s and 6 s, as we can see in the graph above at the bottom of the figure. The fourth part subtracts 2 volts from the waveform between the times. 6 s and 7 s. And finally, the fifth installment subtracts 1 volt from the waveform from time 7 s, determining that f(t), from 7 s , assume the value zero.