Question

After crossing the lake you come to the opposite shore and pass through a door to the next room. The old man is already there in spite of the fact that you clearly went ahead of him. Behind the man are two massive pendulums. Over a period of ten seconds, the pendulum on the left swings three times while the other swings five. ”To open the way forward,” he says, ”the two pendulums must be synchronized. You may alter one of the two pendulums in any way you wish.” How should you proceed? What do you need to change and how much do you need to change it?

Answer 1

Given, the time period of the first(left) pendulum is

& the time period of the second (right) pendulum is

We know the time period of pendulum of length 'L' is given by

let the length of the  first(left) pendulum is 'L₁' & length of the second (right) pendulum is'L₂' .

So the time period of  first(left) pendulum is

&

So the time period of scond (right) pendulum is

.

Two pendulums must be synchronized when T₁ = T₂.

Let we want to alter the length of first (left) pendulum , So that T₁ = T₂. =10/5

Therefore,

Or

So, two synchronize two pendulums, we need to set the length of the first pendulum =