The open loop transfer function of a unity feedback system is \(\mathrm{G}(s)=\frac{\alpha}{s(1+\beta s)}\). For this system overshoot reduces from 0.6 to 0.2 due to change in \(\alpha\) only. Show that

\[
\frac{\beta \alpha_{1}-1}{\beta \alpha_{2}-1} \cong 43
\]

where \(\alpha_{1}\) and \(\alpha_{2}\) are values of \(\alpha\) for 0.6 and 0.2 overshoot respectively.