The displacement time graph of a particle executing SHM is given in...

From graph equation of SHM.

$X = Acos\omegat$
(A) at $\dfrac{3T}{4}$ particle at mean position
$∴ a = 0$
$F = 0$
(B) at T particle again at extreme position so acceleration is maximum
(C) at $t = \dfrac{T}{4},$ particle is at mean position so velocity maximum. $∴ a = 0$
(D) $KE = PE$
$\dfrac{1}{2}k\left({A}^{2} - {x}^{2}\right) = \dfrac{1}{2}k{x}^{2}$
${A}^{2} = 2{x}^{2}$
$x = \dfrac{+ A}{\sqrt{2}}$

$\dfrac{A}{\sqrt{2}} = Acos\omegat$

$t = \dfrac{T}{8}$
$∴ A, B$ and $C$ are correct.