Activity $4$

Problem: Find the response, $c(t),$ to an input, $r(t)=tu(t),$ a unit ramp and assuming zero initial conditions. Given the transfer function represented by

$\frac{dc(t)}{dt}+2c(t)=r(t)$

Answer:

$c(t)=[-\frac{1}{4}+\frac{1}{2}t+\frac{1}{4}{e}^{-2t}]u(t)$