Problem related to Simple Harmonic Oscillations

In summary, Simple Harmonic Motion (SHM) is a type of periodic motion where the amplitude is constant and the motion repeats itself after a certain period, represented by a sinusoidal wave form. In order for a motion to be considered SHM, it must satisfy a specific equation that relates force to displacement-from-equilibrium. This condition can be true even if there is an external influence on the motion.
  • #1
Hareesh
4
0
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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  • #2
What condition needs to be true for a repetitive motion to be simple harmonic?
 
  • #3
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.).
 
  • #4
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...
 
  • #5
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:
 

FAQ: Problem related to Simple Harmonic Oscillations

1. What is the definition of Simple Harmonic Oscillations?

Simple Harmonic Oscillations refer to a type of periodic motion in which a system moves back and forth around a stable equilibrium point with a constant amplitude and a constant period. This type of motion is governed by simple harmonic motion equations, and it can be observed in various physical systems such as a mass-spring system or a pendulum.

2. What factors affect the period of Simple Harmonic Oscillations?

The period of Simple Harmonic Oscillations is affected by two main factors: the mass of the system and the stiffness of the restoring force. A heavier mass or a stiffer restoring force will result in a longer period, while a lighter mass or a weaker restoring force will result in a shorter period.

3. How is the amplitude of Simple Harmonic Oscillations related to its energy?

The amplitude of Simple Harmonic Oscillations is directly proportional to its energy. This means that the higher the amplitude, the more energy the system has. The energy of the system is also affected by the mass and speed of the oscillating object.

4. What is the relationship between Simple Harmonic Oscillations and the motion of a pendulum?

A pendulum is an example of a system that exhibits Simple Harmonic Oscillations. The motion of a pendulum is governed by the same equations as any other system under Simple Harmonic Oscillations, and its period is affected by the length of the pendulum and the acceleration due to gravity.

5. Can Simple Harmonic Oscillations occur in systems with damping?

Yes, Simple Harmonic Oscillations can occur in damped systems. Damping refers to the loss of energy in a system due to external factors such as friction or air resistance. While damping can affect the amplitude and period of the oscillations, the system will still exhibit Simple Harmonic Oscillations as long as the restoring force is proportional to the displacement from equilibrium.

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