Someone asked this question recently:
"Two particles are simultaneously performing SHM along the same path with same time period and equal amplitude A. If the maximum separation b/w particles if (root3)A, then find their phase difference and positions when they cross each other."
This question involves some interesting mathematics. Consider the complex representation of a sinusoid ("Re" denotes "real part" and "j" is the imaginary unit):
Notice that the coefficient on the exponential term is the magnitude of the sinusoid. That will be important to remember. Write general expressions for the two sinusoids under consideration:
Take the difference:
We can therefore infer that the magnitude (peak value) of the resultant sine wave is the magnitude of the complex quantity , which we also know to be . The peak value of the resultant sine wave will occur when the complex exponential has a phase angle that is the negation of the phase angle of , making the argument of the Re() operation simply equal to the length of . The following therefore must be true:
The two sinusoids are therefore separated by plus or minus 120 degrees. The other timing information should be fairly easy to figure out from here.