At t=0 a particle exeucting SHM with a time period 3 s is in phase with another particle executing SHM. The time period of the second particle is T (less than 3 s) . If they are again in the same phase for the third time after 45 s, then the value of T is `cdots `.

Options

A. 1s
B. 1.5 s
C. 2 s
D. 2.5 s

Answer

D

Explanation

Given initially both oscillating particles are in same phase. For keeping calculation simple we assume that they both are at mean positive ( x=0) at t=0. Now first particle is in same phase at given time instances.
t= 0s,3s,6s,9s,12s, 15s,`cdots` etc.
Now we take time period of second particle ( from options ) and select that value of T which gives same phase of both particles at t = 15s, 30s, 45s, `cdots ` etc.
For second particle by option ( a) , t= 0s, 1.5s, 3s,4.5s,6s, `cdots` etc By option (d),
t=0s , 25s,5s, 7.5s, 10s, 12.5s, 15s, `cdots,` etc
So, both particles are in same phase again at t=15s , 30s,45s, `cdots ` etc only when time period of second particle is 2.5 s .