Simple question

Question

For a simple harmonic oscillator, which of the following pairs of the vector quantities cannot both point in the same direction? (THE position vector is the displacement from equilibrium.) A) position and velocity B) velocity and acceleration C) velocity and position D) none of the above

Answer 1

Consider a simple harmonic oscillator in horizontal motion.

 

Since the restoring force vector always points opposite to the direction of the displacement vector, and the acceleration vector points in the same direction as the restoring force vector, then the acceleration vector always points in the opposite direction to the displacement vector, except when they are both zero at the equilibrium point.

Answer 2

Choice (c) is a duplicate of choice (a).  I think you meant choice (c) to be "acceleration and position" because that is the correct answer.

 

Consider a simple pendulum which exhibits SHM when the displacement is small. On the downswing, the acceleration and velocity vectors point down but the position vector points up.  On the upswing, the position and velocity vectors point up but the acceleration vector points down.  So the acceleration always points opposite to the position vector except at equilibrium where they are both zero.

 

In other words, the position vector always points away from the equilibrium position, the acceleration vector always points toward the equilibrium position.