Question

Which of the following relationships between the acceleration a and the displacement x of a particle involve SHM?

(a) a = 0.5x, (b) a = 400x^2, (c) a = -20x, (d) a = -3x^2?

Answer 1

For simple harmonic motion, acceleration is directly proportional to displacement and is directed towards the equilibrium position, that is, opposite to the its direction.

`a \propto -x`

So we can reach at the following conclusions,

a) NO (It is the positive direction)

b) NO (It is the positive direction and it is the square of the distance)

c) Yes (It is the negative address)

d) No (It is the square of the distance)