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:

Position of particle executing SHM: x = A sin(ωt)
Its velocity function is: v = dx/dt = Aω cos(ωt)
Kinetic energy K.E. = (1/2)mv² = (1/2)mA²ω²cos²(ωt) ⇒ K.E. ∝ cos²(ωt)
But at t = T/4, cos(ωT/4) = 0 ⇒ K.E = 0
at t = T/2, cos(ωT/2) = -1 ⇒ K.E is maximum
at t = T, cos(ωT) = 1 ⇒ K.E is maximum