Question

part a

which of the following statements are true?
check all that apply.

all periodic motions are simple harmonic motions.
a system that undergoes periodic motion never has a stable equilibrium position.
simple harmonic motion is periodic motion under the action of a restoring force that is directly proportional to the displacement from equilibrium.
a system that undergoes periodic motion always has a stable equilibrium position.
simple harmonic motion is periodic motion under the action of a restoring force that is inversely proportional to the displacement from equilibrium.

Explanation:

Analyze periodic motion definitions

Using the Vibrational Motion knowledge point
Periodic motion is any motion that repeats itself at regular time intervals. While simple harmonic motion (SHM) is a specific type of periodic motion, not all periodic motions are SHM (for example, a bouncing ball or a planet orbiting a star). Thus, the first statement is false.

Evaluate stable equilibrium requirements

Using the Vibrational Motion knowledge point
For a system to undergo periodic, oscillatory motion back and forth, there must be a restoring force that pulls it back toward a central position. This central position is a stable equilibrium position. Therefore, a system undergoing periodic motion must have a stable equilibrium position. This makes the second statement false and the fourth statement true.

Define simple harmonic motion restoring force

Using the Vibrational Motion and Amplitude knowledge points
By definition, simple harmonic motion is a special case of periodic motion where the restoring force \(F\) is directly proportional to the displacement \(x\) from the stable equilibrium position, acting in the opposite direction:

$$ F = -kx $$

This means the restoring force is directly proportional, not inversely proportional, to the displacement. Thus, the third statement is true and the fifth statement is false.

Answer:

• All periodic motions are simple harmonic motions.
• A system that undergoes periodic motion never has a stable equilibrium position.
• Simple harmonic motion is periodic motion under the action of a restoring force that is directly proportional to the displacement from equilibrium. (Correct answer)
• A system that undergoes periodic motion always has a stable equilibrium position. (Correct answer)
• Simple harmonic motion is periodic motion under the action of a restoring force that is inversely proportional to the displacement from equilibrium.