$[30\%]$ Consider a spring$-$mass system with the following parameters: $m=1{10}^{-3}kg,k=10\frac{N}{m},b=1{10}^{-5}N\frac{S}{m}.$

$(1)$ Calculate the resonant frequency $f_0$ and quality factor $Q.(2)$ Plot the amplitude of the transfer $|H(f)|$ as a function of frequency $($from $1Hz$ to $1000Hz)$ using Matlab or other software $($e$.$g$.,$ Python$).$ The vertical and horizontal axes should be in log scale. Please provide the script.