Try it! - Modal Analysis

Problem

The following system consists of a massless bending beam with length $//<![CDATA[ \begin{array}{l}l\end{array} //]]>$ with a mass attached at its endpoint:

The system matrices with respect to the degrees freedom $//<![CDATA[ \begin{array}{l}\mathbf{u} = \left[w,\varphi\right]^T\end{array} //]]>$ are given as:

with $//<![CDATA[ \begin{array}{l}EI = 1.024 \cdot10^7 \, \mathrm{N m^2}\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}l = 4 \, \mathrm{m}\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}m=1\cdot 10^4 \, \mathrm{kg}\end{array} //]]>$, and $//<![CDATA[ \begin{array}{l}r = 2 \, \mathrm{m}\end{array} //]]>$.