[Charries]

The external force is always opposite to the direction of velocity? or ;
The external force is always opposite to the direction of displacement?

[Stonebridge]

Damping is friction.
Frictional forces always act against motion.
Velocity is the answer.

[Charries]

Thank you Stonebridge.

[Charries]

If I think about SHM and a spring between two horizontal points A, B, with the equilibirum mid point between the two --> when the particle is to the right of the equilibrium, displacement is positive, the velocity is the rate of change in displacement, and is also positive, the force is to the left, in the opposite direction, and hence negative. When the particle is to the left, displacement is negative, rate of change of displacement is negative => velocity is negative, and force is going to the right => and therefore positive.

Is there a situation in SHM when it is true for velocity, but not true for displacement, or is my thinking process above incorrect?

[Charries]

.. NO NO NO - got it, as it comes back from the max amplitude, things change, displacement is still postive, rate of change is negative, and force acts against the velocity ...

[Stonebridge]

(Original post by Charries)
.. NO NO NO - got it, as it comes back from the max amplitude, things change, displacement is still postive, rate of change is negative, and force acts against the velocity ...

Indeed.
When the displacement is to the right (positive, say) then the velocity can be either positive or negative depending on which way it's moving.
When displacement is to the left (negative) the velocity can still be positive or negative.
The frictional force is always in the direction opposite to the velocity. (So it can be in a direction either opposite to or in the same direction as the displacement, depending where the particle is.)