Show me the steps to solve A rotating machine mounted on $4$ equally spaced isolation mounts has an unknown amount of unbalance causing the machine to oscillate. The machine has a total mass M$1=\backslash (\backslash$mathbf$\{300\}\backslash$mathbf$\{$~ k g$\}\backslash )$ and a system natural frequency of $\backslash (\backslash$mathbf$\{18$ ~ H z$\}\backslash )$ along the vertical axis. When the machine is in operation, it will run at a speed range of $15$ to $20$ Hz $.$

$($a$)$ Design a vibration absorber $($i$.$e$.$ Find M$2$ and K$2)$ by tuning the absorber to the machine's natural frequency of $\backslash (\backslash$mathbf$\{18$ ~ H z$\}\backslash ).$ The mass of $\backslash (\backslash$mathbf$\{$M$\}2\backslash )$ must be as small as possible and the effective range of the absorber should be between $15$ to $20$ Hz $.$

$($b$)$ Show the exact peak locations and the effective range of your design from $($a$)$ in a Magnitude Ratio Vs Frequency Graph.