The open loop transfer function of a unity feedback control system is given by [ mathrm{G}(s)=frac{k}{s(s mathrm{~T}+1)}

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The open loop transfer function of a unity feedback control system is given by
\[
\mathrm{G}(s)=\frac{k}{s(s \mathrm{~T}+1)}
\]
(a) By what factor gain \(\mathrm{k}\) should be multiplied so that damping ratio increases from 0.2 to 0.8 ?
(b) By what factor the time constant \(\mathrm{T}\) should be multipled so that damping ratio reduces from 0.6 to 0.3 ?

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