A particle is executing simple harmonic motion with a time period T . At time t = 0 , it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like:

Step-by-step solution

x = A sin ⁡ ω   t v = d x d t = a   ω cos ⁡ ω   t K . E . = 1 2 m   v 2 = 1 2   m   A 2 ω 2 cos 2 ⁡   ω t = 1 2   m   A 2 ω 2 cos 2 ⁡ 2 π T   t At t = 0 , K . E . is maximum. The period of K . E . graph is half of the period of displacement graph. Comment:- The points on the graph of x - axis should be differentiable. In all option mentioned, the graph has cusps at the points on x - axis.