Question

two pendulams have time period T and 5T/4 . they start shm at the same time from the mean position after how many oscillation of the smaller pendulum they will be again in the same phase

Answer 1

Smaller pendulum has less time period & bigger has more

Smaller Pendulum with Time period T will cover = 2π  in T

Bigger Pendulum with Time period 5T/4 will cover 2π in 5T/4

Bigger Pendulum with Time period 5T/4 will cover in T = (2π/(5T/4))* T = 1.6π

Phase difference = 2π - 1.6π = 0.4π

To be in the phase again they should have 2π phase difference

2π/0.4π = 5

5 Oscillation of Pendulum (Smaller) with time period T = 5T = 10π

5T/(5T/4) = 4 Oscillation

4 Oscillation  of Pendulum (bigger)with time period of 5T/4

They will be in phase again