Question

Three simple harmonic motions of equal amplitudes A and equal time periods in the same direction combine. The phase of the second motion is 60° ahead of the first and the phase of the third motion is 60° ahead of the second. Find the amplitude of the resultant motion.

Answer 1

Three SHMs of equal amplitudes ‘A’ and equal time periods in the same dirction combine.
The vectors representing the three SHMs are shown it the figure. Using vector method,
Resultant amplitude = Vector sum of the three vectors = A + A cos 60° + A cso 60° = A + A/2 + A/2 = 2A
So the amplitude of the resultant motion is 2A.