Consider two SHMs along the same straight line x₁=A₁ ( t+ ₁ ) , x₂=A₂ ( t+ ₂ ) , where A₁ and A₂ are their amplitudes and ₁ and ₂ are their initial phase angle. If the two SHMs meet simultaneously and R is the resultant amplitude, match column I with column II.

Step-by-step solution

Given, x₁=A₁ ( t+ ₁ ) and x₂=A₂ ( t+ ₂ ) A: The two SHMs are in phase, A₁=A₂=AR= A₁^2+A₂^2+2 A₁ A₂ =A 2(1+ ) =2 A ( 2 ) where, the phase difference is =0 . R=2 A Therefore, A - III. B :The two SHMs are in phase, A₁ A₂ and phase difference =0 . aligned & R= A₁ ^2+A₂ ^2+2 A₁ A₂ and = 0^ =1 & R= A₁^2+A₂^2+2 A₁ A₂ = (A₁+A₂ ) aligned Therefore, B - I. C: The two SHMs are 90^ out of phase, A₁=A₂=A and phase difference =90^ . R= A₁^2+A₂^2+2 A₁ A₂ = A^2+A^2 =A 2 Therefore, C - IV. D :The two SHMs are 180^ out of phase, A₁=