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.

Question

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.

Infinity Learn · Accepted Answer

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 $$=$$ π$$3$$   ⇒ $$2$$$$π$$$$12$$.t $$=$$ π$$3$$⇒ t $$=$$ $$2s$$

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