A second-order system which has a damping factor of less than $1$ should have an overshoot right?
The formula for this is:
$$\exp{(-\pi*\zeta/\sqrt{1-\zeta^2})}$$
But I have noticed that if the time constant is very large, and the gain is very small, there is no overshoot whatsoever.
In MATLAB's Control System Toolbox, I simulated the transfer function $$g(s) = \frac{4.2}{s(1 + 6.91s)}$$ with a compensator of $K = 0.01$ in a closed-loop circuit with unity feedback. There should have been some overshoot and oscillation since the system is not critically damped, but there isn't!