Question $2[10$ points$]$

A radial saw base, shown in Figure $1,$ has a mass $M=73\mathrm{.}16kg$ and is harmonically driven by a motor that powers the saw's blades. The motor runs at a constant speed and generates a force of $F=13N$ at $180re\frac{v}{m}in$ due to a slight imbalance. This vibrational force was only detected after manufacturing, prompting the need for a vibration absorber to reduce the oscillations in the saw table to zero by retrofitting an absorber onto the base. The absorber must fit within the base structure and should limit deflection to $x_{\text{m}\text{a}\text{x}}=0\mathrm{.}2cm.$ The table legs provide an effective stiffness of $k=2600\frac{N}{m}.$

$2\mathrm{.}1$ Determine the natural frequency of the base $({}_n)$ without the absorber attached

$(03)$

$2\mathrm{.}2$ Determine the mass and stiffness of the vibration absorber$.$

$(07)$

Requirements:

The deflection of the base with the absorber attached should be $x=0$

The system is undamped.