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Two particles P1 and P2 are performing SHM along the same line about the same mean position. Initially they are at their positive extreme position. If the time period of each particle is 12 sec and the difference of their amplitudes is 12 cm then find the minimum time after which the separation between the particles become 6 cm.

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a

5 sec

b

2 sec

c

4 sec

d

6 sec

answer is .

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Detailed Solution

The coordinates of the particles areX1 = A1 cos ωt, x2 = A2 cos ωtseparation = x1-x2 = (A1-A2) cos ωt = 12 cos ωtNow x1 -x2 = 6 = 12 cos ωt⇒ ωt = π3 ⇒ 2π12.t = π3⇒ t = 2s

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Two particles P1 and P2 are performing SHM along the same line about the same mean position. Initially they are at their positive extreme position. If the time period of each particle is 12 sec and the difference of their amplitudes is 12 cm then find the minimum time after which the separation between the particles become 6 cm.