Q140 / 155 · WBJEE 2022 · Physics

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 motion, the phase difference $(\delta)$ between the two motions is

  • A
    $\delta=\frac{\pi}{3}$
  • Correct answer
    B
    $\delta=\frac{2 \pi}{3}$
  • C
    $\delta=\pi$
  • D
    $\delta=\frac{\pi}{2}$

Solution

$A_{\text {res }}^2=A_1^2+A_2^2+2 A_1 A_2 \cos \delta \quad A^2=A^2+A^2+2 A^2 \cos \delta, \cos \delta=-\frac{1}{2} \delta=120^{\circ}$

Hence, the correct answer is option: 'B'.

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