What is the displacement of a particle executing SHM?

What is relation between acceleration and displacement of a particle executing S.H.M?

Velocity and displacement of a particle executing S.H.M. are out of phase by pi/2 . Explain why?

What is displacement of object ?

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct?

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :- y=a sin 2pi t//T (a = maximum displacement of the particle, v = speed of the particle. T= time-period of motion). Rule out the wrong formulas on dimensional grounds.

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :- y=a sin vt (a = maximum displacement of the particle, v = speed of the particle. T= time-period of motion). Rule out the wrong formulas on dimensional grounds.

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :- y=(a//T)sin t//a (a = maximum displacement of the particle, v = speed of the particle. T= time-period of motion). Rule out the wrong formulas on dimensional grounds.