Match List-I with List-II regarding the equations of simple harmonic motion and their corresponding time periods. List-I (Equation of motion) List-II (Time period in s) A. x = 4 (10 t) I. 0.2 B. x = 5 (5 t + 3 ) II. 0.25 C. x = 3 (2 t) + 4 (2 t) III. 0.4 D. x = 8 (4 t) (4 t) IV. 1.0 Choose the correct answer from the options given below:

Step-by-step solution

The time period of a simple harmonic motion is given by T = 2 , where is the angular frequency. A. For x = 4 (10 t) : Comparing with x = A ( t) , we get = 10 rad/s. T = 2 10 = 0.2 s. B. For x = 5 (5 t + 3 ) : Comparing with x = A ( t + ) , we get = 5 rad/s. T = 2 5 = 0.4 s. C. For x = 3 (2 t) + 4 (2 t) : This is a superposition of two SHMs of the same frequency. The resultant equation can be written as x = 5 (2 t + ) . Here, = 2 rad/s. T = 2 2 = 1.0 s. D. For x = 8 (4 t) (4 t) : Using the identity 2 = (2 ) , the eq