A $35$ kg block is supported by a spring and two cantilever beams as shown below. The flexural rigidity of the beams are $E_1{I}_1=8600N{m}^2$ and $E_2{I}_2=24000N{m}^2$ and their masses are $m_1=6\mathrm{.}5$ kg and $m_2=4kg.$The beam length is $l=3m.$ The spring has a stiffness of $k=8k\frac{N}{m}$ and mass $m_s=2\mathrm{.}7kg.$ Determine the fundamental natural frequency of oscillations of the system.

Ans. ${}_n=17\mathrm{.}42ra\frac{d}{s}$