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translational degrees of freedom, vibrational degress of freedom, rotational degrees of freedom. Translational degrees of freedom depends on the dimensional motion of the particle, vibrational degrees of freedom depends on the modes of vibration. Finally, rotational degrees of freedom depends upon the axis of rotations

 

what is the method of counting the squared terms to find the degrees of freedom?

 

the degrees of freedom of a system is given by
f=3N-k
where N=no. of particles
k=no. of constraints.