Show that in SHM the ratio of acceleration and displacement of a particle always remains unchanged .

What quantity remains unchanged in FM wave?

What quantity remains unchanged in AM wave?

The equation x= A sin omega t gives the relation between the time t and the corresponding displacement x of a moving particle where A and omega are constant. Prove that the acceleration of the particle is proportional to its displacement and is directed opposite to it.

Statement I : A particle moving with uniform acceleration has its displacement proportional to the square of time. Statement II : If the motion of a particle is represented by a straight line on the velocity -time graph its acceleration is uniform.

Why are the displacement and the acceleration of a particle executing SHM always in opposite phase?