Q.

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

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a

π/3

b

2π3

c

π6

d

π/2

answer is B.

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Detailed Solution

given  A1=A2=Anet     and      Anet=A Resultant amplitude Anet=A12+A22+2A1A2cosθ ⇒A=A2+A2+2A2cosθ   squaring both side      A2=2A2+2A2cosθ ⇒ 2A2cosθ=-A2 ⇒cosθ=-1/2, ⇒ θ=120∘ ⇒  θ=2π3.
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A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resulting amplitude is equal to the amplitude of individual motions, the phase difference between them is