What is the phase difference between the displacement and acceleration in simple harmonic motion?

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Q: What is the phase difference between the displacement and acceleration in simple harmonic motion?

Solution: In simple harmonic motion, acceleration is always opposite to displacement, hence the phase difference is 180 degrees.

Steps: 6

Step 1: Understand simple harmonic motion (SHM). In SHM, an object moves back and forth around a central point.
Step 2: Identify the two key quantities: displacement (the position of the object from the central point) and acceleration (how quickly the object's velocity is changing).
Step 3: Note that in SHM, when the object is at its maximum displacement (farthest from the center), the acceleration is at its maximum but directed towards the center.
Step 4: Recognize that when the displacement is positive (to one side), the acceleration is negative (towards the center), and vice versa.
Step 5: Conclude that the acceleration is always in the opposite direction to the displacement.
Step 6: Since opposite directions correspond to a phase difference of 180 degrees, we determine that the phase difference between displacement and acceleration in SHM is 180 degrees.