At t=0 , a particle executing 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 .... .

Step-by-step solution

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=0 ~s , 3 ~s , 6 ~s , 9 ~s , 12 ~s , 15 ~s , 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=15 ~s , 30 ~s , 45 ~s etc. For second particle by option (a), t=0 ~s , 1 ~s , 2 ~s , 3 ~s , 4 ~s , 5 ~s , 6 ~s , etc B