If x , v and a denote the displacement, the velocity and the acceleration of a particle executing S H M of time period T . Then, which of the following does not change with time?

Step-by-step solution

We know, instantaneous displacement, x = r   sin ω t ∵ Instantaneous velocity, v = d x d t = r ω   cos ω t So. a T x = - ω 2 x × T x = - ω 2 T = - 4 π 2 T 2 × T = - 4 π 2 T = constant and, ⇒    a T V = - ω 2 r sin ω t × T ω r cos ω t = - ω T tan ω T = - 2 π T × T   tan ω t = not constant Similarly, a T + 2 π v and a 2 T 2 + 4 π 2 v 2 is also not constant, i.e. both are functi