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Two pendulum of time periods 3 s and 7 s...

Two pendulum 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

`(21)/(8) s`

B

`(21)/(4) s`

C

`(21)/(2)` s

D

`(21)/(10) s`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) `y_(1)=A"sin"(omegat+(pi)/(2))implies A"sin"(omegat-(pi)/(2))`
Now, `omega_(1)t+(pi)/(2)=omega_(2)t-(pi)/(2)`
or `t=(pi)/(omega_(2)-omega_(1))=(pi)/((2pi//T_(2))-(2pi//T_(1)))`
`=(T_(1)T_(2))/(2(T_(1)-T_(2)))=(3xx7)/(2(7-3))=(21)/(8)s`
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