Two particles P 1 and P 2 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 s and t

Question

Two particles P 1 and P 2 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 s and the difference of their amplitudes is 12 cm then find the minimum time (in seconds) after which the separation between the particles become 6 cm.

TestHub · Accepted Answer

The x coordinates of the particles are x 1 = A 1 cos ⁡ ω t , x 2 = A 2 cos ⁡ ω t Separation x 1 - x 2 = A 1 - A 2 cos ⁡ ω t = 12 cos ⁡ ω t Now x 1 - x 2 = 6 = 12 cos ⁡ ω t ⇒ ω t = π 3 ⇒ 2 π 12 × t = π 3 ⇒ t = 2 s

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