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

Explanation

Here, `a_(1)=r,a_(2)=r and R=r,theta=?`
As` R^(2)=a_(1)^(2)+a_(2)^(2)+2a_(1)a_(2)costheta`
`:. R^(2)=r^(2)+r^(2)+2r.rcostheta`
`=2r^(2)(1+costheta)`
or `1+costheta=(1)/(2)`
or `costheta =(1)/(2)-1=-(1)/(2)=cos120^(@)`
or `theta=120^(@)=2pi//3radian`