The figure shows a machine with a dynamic vibration absorber$.$ Suppose that the forcing frequency $()$ is close to the system's natural frequency $({}_n).$ The system parameters are given by: $m=10kgk=1000\frac{N}{m},$ and $b=10N\frac{s}{m}.$ If the dynamic vibration absorber is set such that $=\sqrt[\phantom{2}]{\frac{k_a}{m_a}},$ and its mass $(m_a)$ is $20\%$ of the original mass $(m).$

$1-(2$ pts$)$ Use MATLAB to plot the amplitude $x$ and $Y$ versus $$ and determine the two resonance frequencies from the plot.

$2-(1$ pt$)$ What are $x$ and $Y$ amplitudes at the forcing frequency $()?$ Is it possible to set the amplitude $Y=0?$ Justify.