A system described by the following differential equation $$$\frac{d^2y}{dt^2}+3\frac{dy}{dt}+2y=x\left(t\right)$$$ is initially at rest. For input x(t) = 2u(t), the output y(t) is

A causal system having the transfer function $$G\left(s\right)\;=\;\frac1{s\;+\;2}$$ is excited with 10u(t). The time at which the output reaches 99% of its steady state value is

A second-order system has the transfer function $$\frac{C\left(s\right)}{R\left(s\right)}=\frac4{s^2+4s+4}$$. With r(t) as the unit-step function, the response c(t) of the system is represented by

The transfer function of a system is $$G\left(s\right)\;=\;\frac{100}{\left(s\;+\;1\right)\left(s\;+\;100\right)}$$.For a unit step input to the system the approximate settling time for 2% criterion is