A linearly elastic beam of length $2 l$ with flexural rigidity $E I$ has negligible mass. A massless spring with a spring constant $k$ and a rigid block of mass $m$ are attached to the beam as shown in the figure.
The natural frequency of this system is
- $\sqrt{\frac{k l^{3}+6 E I}{m l^{3}}}$
- $\sqrt{\frac{k l^{3}+48 E I}{m l^{3}}}$
- $\sqrt{\frac{6 E I k}{\left(k l^{3}+6 E I\right) m}}$
- $\sqrt{\frac{48 E I k}{\left(k l^{3}+48 E I\right) m}}$