**Introduction **

In a periodic system, the number of vibration frequencies is generally equal to the number of degrees of freedom, which in turn is the minimum number of co-ordinates needed to completely describe its motion. For example, a single pendulum that is constrained to pivot in one plane can have its position specified by a single coordinate (usually angular displacement from the vertical) and has only one natural frequency of vibration. A spring that can pivot around its attachment point has at least two degrees of freedom and therefore two vibration frequencies. The most interesting (and useful) examples of this type are systems with several oscillators that are coupled together. The detailed description of the behavior of such oscillators is described in the link below

Click here to view the file with the description of coupled harmonic oscillators

*References and useful links:*

The above link has been reproduced from the course material at

http://farside.ph.utexas.edu/teaching/315/Waves.pdf

One may also see

http://en.wikipedia.org/wiki/Normal_mode#Example_.E2.80.94_normal_modes_of_coupled_oscillators