Chapter 11, Problem 4Q

For a simple harmonic oscillator, when (if ever) are the displacement and velocity vectors in the same direction? When are the displacement and acceleration vectors in the same direction?

To determine

For a simple harmonic oscillator, when are the displacement and velocity vectors in the same direction andwhen are the displacement and acceleration vectors in the same direction.

Answer to Problem 4Q

Solution:

When going from equilibrium position to maximum displacement (either up ordown), the displacement and velocity vectors point in the same direction.

The displacement and acceleration vectors never point in same direction.

Explanation of Solution

For a simple harmonic oscillator the displacement and velocity vectors are in the same directionwhile the oscillator is moving away from its equilibrium position, one-half of the time. Acceleration vector is always opposite to the position vector, and never in the same direction.