Intersections betweens sinusoids

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SUMMARY

The discussion centers on finding intersection points between two sinusoids defined by different amplitudes, frequencies, and phase differences, represented by the equation A1sin(f1θ + φ1) = A2sin(f2θ + φ2). The original poster indicates that a general solution may not exist and suggests using approximations such as the second-order Taylor series or perturbation series to find solutions near specific points. The complexity of the problem highlights the need for numerical methods or approximation techniques in sinusoidal analysis.

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mnb96
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I'm facing the following problem which sounded simple but apparently it is not (at least for me):

I have two sinusoids: different amplitude, different frequency, different phase difference and I want to find the intersection points, which is equivalent to solving the following equation in [tex]\theta[/tex]:

[tex]A_{1}sin(f_{1}\theta+\phi_{1}) = A_{2}sin(f_{2}\theta+\phi_{2})[/tex]

I was not able either to solve the problem in the general case, nor to find a solution around the net.
 
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I don't believe that a solution formula exists at all, although I cannot prove this claim. I'm afraid you'll have to approximate. For example write the sines as second order Taylor series close to some zero, and solve an approximation there. Or then some kind of perturbation series.

What one should do of course depends on what one wants.
 
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