Two particles are executing SHM with same amplitude and frequency (but with a phase difference). The maximum separation between them was found to be equal to the amplitude. What is the phase difference. This is a question that I came across. And I solved it the following way. Assume one is y1 = A sin (wt) and the other one y2 = A sin (wt + phi) max(y1-y2) = A (given) Solve for phi. Since both y1 and y2 are sinusoids of w frequency, their difference will also be a sinusoid with a different amplitude but with same frequency and a different phase. Since we are just interested in the max value of the difference, I calculated the amplitude of the sinusoid using phasors A e^j(phi) - A. It turned out to be 2A sin(phi/2). From that I calculated phi as pi/3 but the answer I have is as pi/2. I think the book is correct but I could not find the mistake in my calculation. Can some one point out if I am wrong and if yes, where?