Which of these spring systems is equivalent?

MarkH748 · Dec 17, 2009

Hi guys. I looking at a vibrations problem with 2 springs in it (System A). I need to find an overall value for the stiffness K to find the natural frequency of the system. I know that normally when 2 springs are in series I should get the sum of (I/Ki)^-1 which would give me an equivilant stiffness of K/2 in this case (System C). But when I take moments about the pivot point og the rod O it makes more sense to me for it to be 2K (System B). Here are some sketches I made.

Diagram labelled A: a horizontal rigid bar pivoted at point O on its left end, with a spring labelled K above and a spring labelled K below attached to its right end, each anchored to hatched supports.

Diagram labelled B: a horizontal rigid rod pivoted at point O on its left end, with a single spring of stiffness 2K connecting its right end down to a hatched fixed support.

Sketch of a rigid rod pivoted at point O on the left, with a vertical spring labelled K/2 attached at its right end and fixed to a hatched ground line below; the large letter C sits above the rod.

Can anyone shed some light on this as I'm unsure of which system is correct.

Any help would be greatly appreciated.

Mark.

Doc Al · Dec 17, 2009

MarkH748 said:

I know that normally when 2 springs are in series I should get the sum of (I/Ki)^-1 which would give me an equivilant stiffness of K/2 in this case (System C).

Ah... but you don't really have two springs in series, you have one above and one below. Why not derive the effective spring constant for yourself? (Imagine the rod displaced by some Δx. What's the net force on it?)

Which of these spring systems is equivalent?

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