Aparticle vibrates in simple harmonic motion with amplitude. what will be its displacement in one time-period? a 2a 4a 0

'Displacement' is the distance and direction between the starting point and
ending point, regardless of the path followed to get there.

A particle that's executing simple harmonic motion is always in the same place
where it was one time period ago, and where it will be later after another time
period has passed. 

So its displacement during exactly one time period is exactly zero.

Iwould think it is temperature, silica, oxides (gases)