Vibrations problem - Deriving the natural frequencies

[alexisonsmith]

Homework Statement

A thin beam of length L (flexural Stufness EI, cross-sectional area A, density p) is connected to a linear spring of stiffness K_s at each end. Derive the governing equation for the natural frequencies of transverse vibrations from the beam equation and boundary conditions

Homework Equations

Not sure

The Attempt at a Solution

I am really not sure how to start this one, can someone help please

 

[magwas]

Try to use
Flexural stiffness definition (EI=E*I/L),
Hooke's law (F=-kx)
Beam equation
\frac{\partial^2}{\partial x^2}\left(EI \frac{\partial^2 u}{\partial x^2}\right) = w
, in the simple case
EI \frac{d^4 u}{d x^4} = w(x)

See also http://en.wikipedia.org/wiki/Beam_equation