Match List-I with List-II. List-I List-II A. ^2 t I. Periodic with time period T = but not simple harmonic motion (SHM) B. ^3(2 t) II. Periodic with time period T = 2 but Not SHM C. ( t) + ( t) III. Periodic with time period T = and SHM D. t + 2 t IV. Non-periodic Choose the correct answer from the options given below :

Step-by-step solution

For A: y = ^2 t = 1 - 2 t 2 = 1 2 - 1 2 2 t This represents simple harmonic motion (SHM) about the mean position y = 1 2 with an angular frequency of 2 . The time period is T = 2 2 = . Thus, A matches III. For B: y = ^3(2 t) = 3 2 t - 6 t 4 This is a superposition of two SHMs with angular frequencies 2 and 6 . It is periodic but not SHM. The time period is the LCM of T₁ = 2 2 = and T₂ = 2 6 = 3 , which is T = . Thus, B matches I. For C: y = ( t) + ( t) The angular frequencies are ₁ = and ₂ = . The ratio ₁ ₂ = 1 is