I will show how to do it using an example and then you can generalize it.
So amplitude in this case would be .
I'm having some troubles determining the amplitude/magnitude of the following equation.
Since each part is at a different frequency, i cannot sum the magnitudes of each part.
I have also thought about using variations of the double/triple angle formulae and some basic trigonometric identities, so that I can write the equation under a single frequency, but by doing so, I am introducing some higher order terms, which seem to negate the ability to sum the amplitudes together.
For example, the term with would look like
I suppose another method would be to plot the first equation and then record the amplitude, but i would like a more generalised approach to solve this problem. All input is welcome and appreciated.
Thanks for your answer. I actually have a question about this. When you found that it is , is this a peak value or the average value? I plotted your example in matlab, and found that the peak amplitude value is 3. What is this method that you are using? Could you please further explain your method?
Thanks for your help.
Sorry I must have made a mistake there.
I'm having some trouble visualizing how to do it for three terms. im assuming the magnitude can be found by . But when you have to break it down into cosine and sine terms, it seems to be quite difficult. If A = 1, B = 2 and C = 3, i can see that maybe you can break the C term into A+B, but for the general case, this is not so simple. Please advise.
I am extremely sorry.The method I described above works only when the frequencies are same,but amplitudes are different.
In general case,it is not possible to write it as a simple sine or cosine formula.