A particle is subjected to two simple hasrmonic motions 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.

Explanation

Let the amplitudes of the individual motions be `A` each. The resultant amplitude is also `A`. If the phase differnce between the two motions is `delta`,
`A = sqrt(A^(2) + a^(2) + 2A. A. cosdelta)`
`A = Asqrt(2(1 + cosdelta)) = 2Acos'(delta)/(2)`
`cos'(delta)/(2) = (1)/(2)`
`delta = 2pi//3`