A particle is subjected to two simple harmonic 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 ampitudes of the individual motions be A each. The resultant asmplitude is also A. If the phase difference between the two motion is delta
`A=sqrt(A^2+A^2+2A.A.cosdelta)`
or `=Asqrt(2(1+cosdelta))=Acosdelta/2`
or `cosdelta/2=1/2`
`or delta=2pi/3`