Two pendulums of same amplitude but time periods 3s and 7s start oscillating simultaneously from two opposite extreme positions. After how much time (s) they will be in phase?

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$\frac{21}{4} s$

$\frac{63}{8} s$

$\frac{21}{2} s$

$\frac{21}{8} s$

answer is A, D.

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Detailed Solution

$y_{1} = a \cos ω_{1} t a n d y_{2} = a \cos (π + ω_{2} t)$
For same phase $ω_{1} t = π + ω_{2} t$
$t = \frac{π}{ω_{1} - ω_{2}} = \frac{π}{\frac{2 π}{3} - \frac{2 π}{7}} = \frac{21}{8} s$
Or $t = \frac{3 π}{ω_{1} - ω_{2}} = \frac{3 π}{\frac{2 π}{3} - \frac{2 π}{7}} = \frac{63}{8} s$

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