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  1. If you have an $N$ degrees of freedom system what does this mean?

  2. What is the difference between a 1 and a 2 degrees of freedom system?

Qmechanic
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    Possible duplicates: http://physics.stackexchange.com/q/8860/2451 and links therein. – Qmechanic Nov 03 '14 at 08:06
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    have a look at this wiki article http://en.wikipedia.org/wiki/Degrees_of_freedom_%28physics_and_chemistry%29 – anna v Nov 03 '14 at 10:04

2 Answers2

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For example an object can vibrate in one dimension only (e.g $x$, thus $1$ degree of freedom).

Or an object can vibrate in 2 dimensions (e.g $x$ and $y$, $2$ degrees of freedom)

Furthermore an object can vibrate in a rotational sense, a further degree of freedom (in this case an angle lets say $\phi$, in a classical sense and not a quantum-mechanic sense).

References:

  1. http://en.wikipedia.org/wiki/Degrees_of_freedom_%28physics_and_chemistry%29

  2. http://en.wikipedia.org/wiki/Normal_mode

  3. http://en.wikipedia.org/wiki/Rotation

  4. http://en.wikipedia.org/wiki/Molecular_vibration

Nikos M.
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One degree of freedom is a straight line between 2 points. It has no width and no plane in which to vibrate. A line between 2 points involves distance which implies time. Assuming that time is a dimension a straight line requires time and a 2 dimensional plane in which to vibrate. Hence, three dimensions are required to allow the simplest of vibrations. Four dimensions allow a simple vibration to rotate, and so on up. String theory allows more complex wave functions in higher dimensions, each requiring their own manifolds (higher dimensional spaces).

David Clover
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