Two pendulums of time period 3s and 7s respectively start oscillating simultaneously from two opposite extreme positions. After how much least time they will be in phase

Question

Two pendulums of time period 3s and 7s respectively start oscillating simultaneously from two opposite extreme positions. After how much least time they will be in phase (A) (21/8)s (B) (21/4)s (C) (21/2)s (D) (21/10)s

Tardigrade Admin · Accepted Answer

Let they will meet in phase after time 't' . Then φ1-φ2=π (2 π /T1)t-(2 π /T2)t=π ⇒ t=(21/8)s

Q. Two pendulums of time period $3 s$ and $7 s$ respectively start oscillating simultaneously from two opposite extreme positions. After how much least time they will be in phase

$\frac{21}{8} s$

$\frac{21}{4} s$

$\frac{21}{2} s$

$\frac{21}{10} s$

Let they will meet in phase after time $^{'} t^{'}$ .
Then $ϕ_{1} - ϕ_{2} = π \frac{2 π}{T _{1}} t - \frac{2 π}{T _{2}} t = π \Rightarrow t = \frac{21}{8} s$

Q. Two pendulums of time period 3s and 7s respectively start oscillating simultaneously from two opposite extreme positions. After how much least time they will be in phase

821​s

421​s

221​s

1021​s