$1.$ Consider that a mechanical vibration isolation system has the transfer function: $($s$)=2$s $+5$ s$($s $2+2$s $+25)$ a$.$ Derive the analytical frequency response $($magnitude and phase$)$ in decibels and degrees. b$.$ Sketch the Bode diagram using the asymptotic approximation rules and the provided log paper. c$.$ Based on the results from part $($b$),$ what is the range of frequencies for which this system is rated, if the system$$s designer advertises attenuation greater than $50\%?$

Consider that a mechanical vibration isolation system has the transfer function:

G$($s$)=(2$s$+5)/($s$($s$^(2)+2$s$+25))$

a$.$ Derive the analytical frequency response $($magnitude and phase$)$ in decibels and degrees.

b$.$ Sketch the Bode diagram using the asymptotic approximation rules and the provided log paper.

c$.$ Based on the results from part $($b$),$ what is the range of frequencies for which this system is rated, if

the system's designer advertises attenuation greater than $50\%?$