Two pendulums of time periods 3s and 7s respectively start oscillating simultaneously from two opposite extreme positions. After how much time they will be in same phase?
A
218s
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
214s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
212s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2110s
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A218s 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(ω2t−π2)...(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=ω2t−π2 ⇒t=πω2−ω1
Substituting ω=2πT ⇒t=T1T22(T1−T2)=7×32(7−3) ∴t=218s