Problem related to Simple Harmonic Oscillations

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A ball falling through a 'V' shaped curve exhibits simple harmonic motion (SHM) under specific conditions. For motion to be classified as SHM, it must have a constant amplitude, a consistent period, and be periodic in nature. The key factor is the relationship between the restoring force and the displacement from the equilibrium position, which can be described by a specific equation. This equation defines the conditions necessary for the motion to be considered simple harmonic. Understanding these principles is essential for proving that the motion in question is indeed SHM.
Hareesh
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A ball falling through a 'V' shaped curve attains Simple Harmonic Oscillations or not. If yes give equation.
Yes it is simple harmonic oscillation. But how i can prove it.
 
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What condition needs to be true for a repetitive motion to be simple harmonic?
 
Amplitude is constant and period and no external influence.Any motion that repeat itself after a certain period is known a (periodic) motion and since a motion can be represent in a sinusoidal wave form, (i.e. sine & cosine) it is called harmonic motion. The simplest type of such harmonic vibration is called simple harmonic motion (s.h.m.).
 
OK... that's a decent description of what the motion looks like. But there's a condition in physics that will always lead to the type of motion you describe if the condition is true.

It has something to do with the force an object experiences, and the object's displacement from equilibrium position...
 
Welcome to PF!

Hi Hareesh! Welcome to PF! :smile:
Hareesh said:
Amplitude is constant and period and no external influence.Any motion that repeat itself after a certain period is known a (periodic) motion and since a motion can be represent in a sinusoidal wave form, (i.e. sine & cosine) it is called harmonic motion. The simplest type of such harmonic vibration is called simple harmonic motion (s.h.m.).

"No external influence" doesn't matter … shm is a description of a type of movement, and it doesn't matter what causes it. :wink:

Periodic motion is simple harmonic only if it satisfies a particular equation, which as heth :smile: says, relates force to displacement-from-equilibrium.

What is that equation? :smile:
 

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