For a particle executing simple harmonic motion, the time period...

Let the time period of the simple harmonic motion be $T$.

At the mean position, the particle crosses the point twice in one complete oscillation. The time interval between consecutive appearances is $\dfrac{T}{2}$.

At any point between the mean position and an extreme position, the particle crosses the point twice in one complete oscillation, while moving in opposite directions. The time intervals between consecutive appearances alternate between $t$ and $T-t$, neither of which is equal to $T$.

At an extreme position, the particle reaches the point only once in one complete oscillation. The time interval between consecutive appearances is exactly equal to the time period $T$.