At two particular closest instants of time $t_{1}and{t}_2,$ the displacement of a particle performing SHM are equal. At these instants

As the phase of any body is SHM will be increasing continuously and it will not be equal for any two instants.

As the total energy of the body is constant, when the displacements are equal the instantaneous speed will also be the same.

And the accelerations will be same at the two instants.