# Oscillation find frequency of small oscillation of a thin uniform vertical rod of mass M and length L when its upper end is hinged and lower end attached to a spring of stiffness K on either side of the rod,the free end of each spring connected to wall.

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Does this help, it may be a start.
A Cos[w t - è[t]] + B è''[t]==0, where A and B are arbitrary constants?

If you expand the Cosine term, you get A Cos[w t] Cos[è[t]] + A Sin[w t] Sin[è[t]] +B è''[t] ==0, which can be approximated as:

B è''[t] + A Sin[w t] è[t]== -A Cos[w t]

So is the frequency of small oscillations just Sqrt[(A Sin[w t])/B]?

Posted on Nov 07, 2007

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Posted on Jan 02, 2017

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See Figures 1, 2 and 3
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