My Math Forum amplitude of a sinusoid

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 April 30th, 2012, 09:49 PM #1 Newbie   Joined: Apr 2012 Posts: 1 Thanks: 0 amplitude of a sinusoid I *think* this is the correct place to put this question. But here goes: I'm having some troubles determining the amplitude/magnitude of the following equation. $A\cos(2\omega t+\beta_1)+B\cos(3\omega t+\beta_2)+C\cos(5\omega t+\beta_3)$ 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 $5\omega$ would look like $16\cos^5(\omega t)-20\cos^3(\omega t)+5\cos(\omega t)$ 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.

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