1l c m of 1/f1 and 1/f2
Two pendulums with natural frequencies f1 and f2 are released in phase at same instant of time. After what interval will they come in phase again?
a) 1/f1 + 1/f2
b) 1/f1 - 1/f2
c) 1/(f1.f2)
d) L.C.M of 1/f1 and 1/f2
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4 Answers
71Ok.
@Rancho6
See, WE know that T = 1/f , where is Time period of the respective pendulums.
So we have T1 and T2 as the Time period of the two pendulums. Now as said they start is phase at t = 0.
Obviously, they will again be in the same phase when the time taken by both to reach any particular position (the point where they are in same phase) should be such that it common to both i.e., LCM of T1 and T2.
eg.,
Say Time period of two pendulums are 10 sec and 20 sec.
At t = 0, Both in phase
At t = 10, A has completed one oscillation while B is halfway. (??)
At t = 20, A will complete its second oscillation while B will complete it first. (Now both pendulums here at in same phase).
...
Similarly for any such time interval you can say the same.
Hence Answer is LCM of T1 and T2 or LCM of 1/f1 and 1/f2.
