Rotating Vectors and
Sinusoidal Waveforms Tutorial

What it teaches: This interactive tutorial teaches the concept of a rotating vector and how it generates a sinusoidal waveform. It uses animation to illustrate a topic that is very difficult to illustrate on a written page. Here is a screen shot of the contents:

The purpose of part 1 is to make you familiar with the sin curve. When you are finished you will know how to solve an equation of the form:

for all values of t, given the parameters A, and .

Then in part 2, via animation, you are introduced to rotating vectors and the concepts of angular velocity and phase angle.

In part 3 you see the waveforms that correspond to the rotating vectors.

In part 4 you see animations of various cases of the addition of sinusoidal waves, including Fourier series.

How it works: By double-clicking on a topic in the table of contents you jump to the screen associated with that topic. In each screen there is text on the right side explaining some concept and graphics on the left illustrating the concept. Most topics have a 'try it yourself' section where you can create your own examples.

Here is a screen shot from the topic Sinusoidal waveforms - try to find the equation of this waveform yourself. By using the scroll bars you can adjust the values of the parameters
, f, T, and A of the green waveform and try to make the green waveform identical to the (randomly generated) red waveform. This will help you understand the role of each of the parameters.


Here is a screen shot from the topic Addition of sinusoidal waveforms - rotating vectors with the same angular velocity. This topic illustrates the method of phasor addition (that you can add waveforms indirectly by adding the rotating vectors that generate them).

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