Two pendulums A and B start swinging side by side simultaneously from mean position in the same direction. A takes  and B takes  to reach the first extreme point. Find the ratio of number of oscillations of A to B, when both reach again at mean position simultaneously in same time.
Answers
Given : Two pendulums A and B start swinging side by side simultaneously from mean position in the same direction
A takes  A sec and B takes  B sec to reach the first extreme point.
To Find : ratio of number of oscillations of A to B, when both reach again at mean position simultaneously in same time
Solution:
A takes  A sec to reach the first extreme point.
Hence Every 2A secs to reach at Mean position
& 4A secs to complete an Oscillation
B takes  B sec to reach the first extreme point.
Hence Every 2B secs to reach at Mean position
& 4B secs to complete an Oscillation
To Find the time to Meet again
we need to find LCM of 2A & 2B
= 2 LCM ( A , B)
Oscillation by A = 2 LCM ( A , B) / 4A = LCM ( A , B) / 2A
Oscillation by B = 2 LCM ( A , B) / 4B = LCM ( A , B) / 2B
Ratio of number of oscillations of A to B = (LCM ( A , B) / 2A)/ (LCM ( A , B) / 2B)
= B / A
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