Condition for Simple Harmonic Motion

In summary, the conversation discusses finding the minimum R/r ratio for a small object mounted on the perimeter of a hoop to perform simple harmonic motion when placed in a fixed semi-cylinder shaped rough trough. The idea is to find the stable equilibrium position where the object's potential energy is minimum, which has been discussed in a previous forum post. The person decides not to pursue the problem further due to its complexity.
  • #1
utkarshakash
Gold Member
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Homework Statement


a small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that the small mass is at the top. Find the least R/r ratio such that the object performs simple harmonic motion.

The Attempt at a Solution



For the object to perform SHM it must be in a stable equilibrium position. So, its potential energy must be minimum at the mean position. But how do I express it mathematically?
 
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  • #3
Pranav-Arora said:
You have the right idea. I discussed the very same problem in past here.

Look: https://www.physicsforums.com/showthread.php?t=663246

Hmm that's a really long post and I think I should better leave this question as it would be too time consuming. btw Thanks for help!
 

Related to Condition for Simple Harmonic Motion

1. What is the condition for simple harmonic motion?

The condition for simple harmonic motion is that there must be a restoring force acting on the object that is proportional to its displacement from its equilibrium position and directed towards the equilibrium position.

2. How is the condition for simple harmonic motion related to Hooke's Law?

Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. This is the same condition required for simple harmonic motion, as the restoring force must be proportional to the displacement of the object.

3. Can an object exhibit simple harmonic motion without a restoring force?

No, an object cannot exhibit simple harmonic motion without a restoring force. This is because the restoring force is what causes the object to oscillate back and forth around its equilibrium position.

4. What happens if the condition for simple harmonic motion is not met?

If the condition for simple harmonic motion is not met, the object will not exhibit simple harmonic motion. Instead, it may exhibit other types of motion such as linear or circular motion.

5. Are there any real-life examples of objects exhibiting simple harmonic motion?

Yes, there are many real-life examples of objects exhibiting simple harmonic motion. Some common examples include pendulums, mass-spring systems, and vibrating guitar strings.

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