Differential equations (Laplace transform

We know that $A$ is the magnitude $|H|$, while the magnitude graph gives us $20\log_{10} |H|$. So $$20\log_{10} |H|=-22.8\implies \log_{10} |H|=-1.14 \implies A=|H|=10^{-1.14} $$
The phase graph gives us $$\phi =38 \deg = {38\over{180}}\pi \textrm{ radians}$$ Also, the frequency on the graphs is $$\omega = 0.885$$