What is the phase difference between the displacement and acceleration of a simple harmonic oscillator?

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Q: What is the phase difference between the displacement and acceleration of a simple harmonic oscillator?

Solution: In simple harmonic motion, acceleration is 180 degrees out of phase with displacement.

Steps: 6

Step 1: Understand what a simple harmonic oscillator is. It is a system that moves back and forth in a regular pattern, like a swinging pendulum or a mass on a spring.
Step 2: Know that in simple harmonic motion, the position (displacement) of the object changes over time.
Step 3: Recognize that acceleration is how quickly the velocity of the object is changing.
Step 4: Learn that in simple harmonic motion, when the displacement is at its maximum (the object is farthest from the center), the acceleration is at its maximum in the opposite direction.
Step 5: Realize that this means when displacement is positive, acceleration is negative, and vice versa.
Step 6: Conclude that the phase difference between displacement and acceleration is 180 degrees, meaning they are in opposite directions.