Question $5$

$[20]$

a$.$ A boat traveling on the waves in a river follows a second$-$order system which has a natural angular frequency of $2\mathrm{.}0$ Hz and a damped frequency of $1\mathrm{.}8$ Hz

Calculate $($a$)$ The damping ratio, $($b$)$ Rise time, $($c$)\%$ Overshoot $($OS$),($d$)t_g.$

b$.$ What will be the state of damping of a system having the following transfer function and subject to a unit step input?

$G(s)=\frac{1}{s^2-3s-10}$

c$.$ Expand the following equation of Laplace transform in terms of its partial fractions and obtain its time$-$domain response.

$Y(s)=\frac{2s}{(s+1)(s+2)}$