Question: Solving multiple phase angles for multiple equations

Greetings All

I have several equations and each have their own individual frequencies and amplitudes. I would like to sum the equations together and adjust ONLY the individual phases, phase1,phase2, and phase3 to keep the total amplitude value of eq_total under a specific value like 0.8. I know I can normalize the signal or change the vertical offset, but for my purposes I need to have the amplitude controlled by changing/finding the values for just the phases in phase1,phase2, and phase3 that will do this.


=0.2*cos(2pi*t*3+phase1)+vertical offset1
=0.7*cos(2pi*t*9+phase2)+vertical offset2
=0.8*cos(2pi*t*5+phase3)+vertical offset3


Is there a way to solve for phase1,phase2, and phase3 so that the amplitude of the summed signals in eq_total never goes over 0.8 by just adjusting/finding the values of phase1,phase2,and phase3?

Do I have to use for loops to run through each phase and do a test?



Here's a picture of a geogebra applet I tested this idea with.

Use phase the change amplitude





Here's a link to the file if you want to interact with it in geogebra (the latest geogebra is needed)

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