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Question

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

A
218 s
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B
214 s
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C
212 s
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D
2110 s
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Solution

The correct option is A 218 s
Equation of displacement of pendulums performing SHM and starting from extreme position is,

pendulum 1: y1=Asin(ω1t+π2) ...(1)
Equation of motion of pendulum 2: y2=Asin(ω2tπ2) ...(2)
Since on putting t=0 we get y1=A, & y2=A

For the pendulums to vibrate in same phase :
Δϕ=0
ϕ1=ϕ2
ω1t+π2=ω2tπ2
t=πω2ω1
Substituting ω=2πT
t=T1T22(T1T2)=7×32(73)
t=218 s

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