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Question

# Two particles P and Q start from the origin and execute simple harmonic motion along x – axis with the same amplitude and time periods 3 s and 6 s respectively. The ratio of the velocities of P and Q when they meet is

A
1:2
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B
2:1
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C
2:3
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D
3:2
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Solution

## The correct option is B 2:1x1=Asin(w1t) , w1=2π3,w2=2π6 x2=Asin(w2t) when the particles meet each other their positions are equal x1=x2→sin(w1t)=sin(w2t) →w1t=π−w2t →(w1+w2)t=π→t=1s v1=Aw1cos(w1t) , v2=Aw2cos(w2t) ∴v1v2=w1w2×cos(2π3)cos(π3)=21

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