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

In summary, the maximum acceleration of a pendulum with an amplitude of 2m is always a positive value, as determined by the equation (2*pi*frequency)^2 * amplitude. However, the actual acceleration is a vector and can have different directions depending on the sign of its components. The book did not mention this, but it is an important concept to note.
  • #1
pyman12
5
0
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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  • #2
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.
 
  • #3
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.
 

1. What is simple harmonic motion?

Simple harmonic motion refers to the periodic back-and-forth motion of an object around a central equilibrium point, caused by a restoring force that is directly proportional to the displacement from the equilibrium position.

2. Why does simple harmonic motion occur?

Simple harmonic motion occurs when an object experiences a restoring force that pulls it back towards the equilibrium position after being displaced. This force is usually caused by a spring or elastic material.

3. What is maximum displacement in simple harmonic motion?

Maximum displacement in simple harmonic motion refers to the farthest distance an object moves from its equilibrium position during one cycle of motion.

4. Why is acceleration positive at maximum displacement?

The acceleration is positive at maximum displacement because at this point, the velocity of the object is changing from positive to negative, meaning it is accelerating in the opposite direction. This acceleration is caused by the restoring force pulling the object back towards equilibrium.

5. How does amplitude affect simple harmonic motion?

The amplitude, or maximum displacement, of an object in simple harmonic motion determines the maximum speed and acceleration of the object. A larger amplitude results in a larger maximum speed and acceleration, while a smaller amplitude results in a smaller maximum speed and acceleration.

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