Answer to Question #165821 in Physics for Cristian Constantinescu

Question

A simple pendulum of time period 1.90 s is set up alongside another pendulum of time period 2.00 s. The pendulums are displaced in the same direction and released at the same time. Calculate the time interval until they next move in phase. 

Answer 1

'Move in phase' means that at a moment they become at the same position (angle relative to the vertical).

So, in our problem the motion of each bob will not be synchronous. But after 20 seconds the first one will make 10 oscillations and the other one - 10.5. After 30 seconds the first one will do 15, the other one 15.8. Then, finally, after 38 seconds the first one will make 19 complete oscillations and the other one 20 complete oscillation. Thus, the next time they move in phase will be after 38 seconds.