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

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.

What quantity remains unchanged in FM wave?

What quantity remains unchanged in AM wave?

What will be the percentage increases or decrease in the value of acceleration due to gravity on the surface of the earth , if the radius of the earth decreases by 1% and the mass of the earth remains unchanged ?

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?