Peak of two sine waves (fundamental and phase shifted 2nd harmonic)

[ssthakur1@sheffield.ac.uk]

I am trying to find the maximum and minimum peaks of a function which goes as:

y=x1 cos(f1+ teta) + x2 cos(2*f1);

The peak values are straightforward for cases where the frequencies are equal or when they are non-multiples. I am having trouble to quantify the maximum and minimum values of 'y'.

Note: teta, x1 and x2 all these vary from time to time. I am therefore looking for a generalised expression (accuracy <5%).

 

Thanks in advance.

[mathematic]

I'll assume f1 should be f1t.  Elementary calculus gives x1sin(f1t+teta)+2x2sin(f2f1t)=0  as the equation to be solved for t.  Good luck!.