Two particles P and Q describe SHM of same amplitude a and same frequency f along the same straight line. The maximum distance between the two particles is a 2 . The phase difference between the particle is

Step-by-step solution

Given that, two particles P and Q describes SHM of same amplitude a and frequency f . Let equation of motion of two particles are x₁=a t and x₂=a ( t+ ) where, be the phase difference. Path difference, aligned & x₂-x₁=a ( t+ )-a t & x₂-x₁=2 a ( t+ - t 2 ) ( t+ + t 2 ) aligned aligned & [ Using identity A- B=2 ( A-B 2 ) ( A+B 2 ) ] & x₂-x₁=2 a ( 2 ) ( t+ 2 ) aligned The distance x₂-x₁ will be maximum when ( t+ 2 )=1 Maximum distance, aligned x₂-x₁ & = 2 a & =2 a 2 2 & = 1 2 2 = 45^ 2 & =45^ aligned Phase difference,