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.