E-StoreSIMPLE HARMONIC MOTION
6 Jan 2009 20:26:46 IST
SIMPLE HARMONIC MOTION
Simple Harmonic Motion
Idea: Any object that is initially displaced slightly from a stable equilibrium point will oscillate about its equilibrium position. It will, in general, experience a restoring force that depends linearly on the displacement x from equilibrium:
Hooke's Law:
| Fs = - kx | (1) |
where the equilibrium position is chosen to have x -coordinate x = 0 and k is a constant that depends on the system under consideration. The units of k are:
[k] =  . | (2) |
Definitions:
- Amplitude ( A ): The maximum distance that an object moves from its equilibrium position. A simple harmonic oscillator moves back and forth between the two positions of maximum displacement, at x = A and x = - A .
- Period ( T ): The time that it takes for an oscillator to execute one complete cycle of its motion. If it starts at t = 0 at x = A , then it gets back to x = A after one full period at t = T .
- Frequency ( f ): The number of cycles (or oscillations) the object completes per unit time.
f = 
. (3)
The unit of frequency is usually taken to be 1 Hz = 1 cycle per second. - Simple Harmonic Oscillator: Any object that oscillates about a stable equilibrium position and experiences a restoring force approximately described by Hooke's law. Examples of simple harmonic oscillators include: a mass attached to a spring, a molecule inside a solid, a car stuck in a ditch being ``rocked out'' and a pendulum.
Note:
- The negative sign in Hooke's law ensures that the force is always opposite to the direction of the displacement and therefore back towards the equilibrium position (i.e. a restoring force).
- The constant k in Hooke's law is traditionally called the spring constant for the system, even when the restoring force is not provided by a simple spring.
- The motion of any simple harmonic oscillator is completely characterized by two quantities: the amplitude, and the period (or frequency).
Comments (2)
anchal singhal
Blazing goIITian
Joined: 21 Aug 2008 19:28:35 IST
Posts: 380
6 Jan 2009 21:12:04 IST
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plz comment
7 Jan 2009 10:32:56 IST
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sorry if i am being rude but let alone IIT aspirants, those who are not even preparing for JEE know that. if you have to earn nickels, you should post something new and original, like a new approach to a question, how to understand a concept, or much better, how to study inorganic. but that should be original. or you could just post your doubts here and we will always be there to help you.
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