Simple Harmonic Motion: Why is acceleration positive at maximum displacement?

AI Thread Summary
In simple harmonic motion, maximum displacement occurs at the amplitude, where the restoring force acts towards equilibrium, resulting in negative acceleration. However, the maximum acceleration calculated using the formula (2*pi*frequency)^2 * amplitude is a positive value, representing its magnitude. The actual acceleration is a vector quantity that can have both positive and negative components depending on its direction. This distinction between magnitude and direction is crucial for understanding the behavior of acceleration in harmonic motion. Clarifying this concept helps reconcile the apparent contradiction in the interpretation of acceleration at maximum displacement.
pyman12
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For example, I have a pendulum with amplitude of 2m, when the pendulum is at a displacement of 2m, wouldn't the acceleration be negative as the restoring force is acting towards equilibrium? The equation I am taught is that maximum acceleration is (2*pi*frequency)^2 * amplitude, which is a positive value?
 
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pyman12 said:
The equation I am taught is that maximum acceleration is (2*pi*frequency)^2 * amplitude, which is a positive value?
It's the maximal magnitude of acceleration, which always positive. The actual acceleration is a vector, which can point in different directions, depending on the sign of it's components.
 
A.T. said:
It's the maximal magnitude of acceleration, which always positive. The actual acceleration is a vector, which can point in different directions, depending on the sign of it's components.
Oh I see, the book didn't mention that. Thanks.
 

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