Question

A particle is subjected to two simple harmonic motion in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the amplitude of the individual motions. Find the phase difference between the individual motions.

Answer 1

Let the amplitudes of the individual motion be A each. The resultant ampliotude is also A. If the phase difference between the two motion is `sigma`
`A = sqrt(A^(2) + A^(2) + 2 A A cos sigma)`
or `= A sqrt(2 (1 + cos sigma) = 2 A cos ((sigma)/(2))`
or `cos ((sigma)/(2)) = (1)/(2)`
or `sigma = 2 pi//3`