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I would like to know why in the context of vibrating systems, we define degrees of freedom in terms of number of independent coordinates (by coordinates I mean the numbers which specify the components of vectors) required to specify the motion instead of the configuration (configuration refers to just the positions and not velocities). Are these definitions equivalent because for motion, we are always concerned with the rate of change of each coordinate (describing the position or configuration) and thus motion also ends up involving same number of coordinates to describe the motion?

The book I am reading also mentions a line saying

On occasion, when internal forces are carried as unknowns, the number of equations exceeds the number of degrees of freedom by the number of unknown forces.

I am not able to see where would such a need arise; an example of this would be greatly appreciated.

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  • $\begingroup$ OP's 1st subquestion seems to be essentially a duplicate of What is the definition of how to count degrees of freedom? and just a matter of different conventions. $\endgroup$ – Qmechanic Mar 30 at 18:55
  • $\begingroup$ @Qmechanic It may well be but I honestly can’t seem to understand it (perhaps because I don’t understand all the terms used therein); my doubts are why is DOF number of initial conditions by 2? And how does it show equivalence between the two definitions/conventions? $\endgroup$ – ModCon Mar 31 at 5:49

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