Question

In a simple harmonic motion, which of the following pairs of quantities are always oriented in mutually opposite directions?

1. Restorimg force and acceleration.
2. Restoring force and displacement.
3. Velocity and displacement.
4. Acceleration and displacement.

Answer is : 2 and 4

Answer 1

Relationship between Force acting`(F)` and displacement`(x)` of a particle undergoing SHM is expressed as,

`f = -k.x`

so, clearly force is acting against the direction of displacement.

and,acceleration is given as,

`a = F/m = -(k/m)x` where, `(k/m)` is constant

so,acceleration due to the applied force also acts against the direction of displacement.

again, accelartion occurs in the direction of force applied,because accelertion occurs due to the application of force and direction of velocity is also along the displacement. ( ref. `v=omega*sqrt(A^2 - x^2)`)