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I want to be able to be able to get the amplitude of the following function:

$||A||\cos(2 \omega t + a)+||B||\cos(3 \omega t +b)+||C||\cos(5 \omega t +c)$

I am trying to find a way to get the amplitude of this function. This is usually simple for when there is one value of $\omega$ to consider, but I'm having a hard time thinking how to go about this.

One thing I did try was to just sum $||A||, ||B||, ||C||$ together. If we ignore the phases a, b, c, this gives an idea of what the max value obtained is, but I don't think it aptly describes the amplitude of the function as it is not sinusoidal in the traditional sense and most of the time, is below this max value. I noted that that min value is not equal to the negative of the max value either.

I played around with the RMS $\sqrt{||A||^2+||B||^2+||C||^2}$ but i'm sure if that is an appropriate approach.

Suggestions?

  • 0
    [Here's an example with a function of your form.](http://www.wolframalpha.com/input/?i=plot%20cos%202t%20%2b%20cos%203t%20%2b%20cos%205t,%20sqrt%28%28cos%202t%20%2b%20cos%203t%20%2b%20cos%205t%29%5E2%20%2b%20%28sin%202t%20%2b%20sin%203t%20%2b%20sin%205t%29%5E2%29,%20-sqrt%28%28cos%202t%20%2b%20cos%203t%20%2b%20cos%205t%29%5E2%20%2b%20%28sin%202t%20%2b%20sin%203t%20%2b%20sin%205t%29%5E2%29)2012-05-12

0 Answers 0