A question on the response of an RC circuit and pole of its transfer function
You are just producing plots that show the real world and not the underlying maths that lies behind the s-plane. Basically you are thinking in terms of time equivalence of bode plots when you should be thinking in terms of poles and zeros. Hopefully this picture of a 2nd order low pass filter will help: -



The three pictures along the top show the bode plots of three low pass filters where damping is getting less from left to right.

The bottom left picture shows a 3D view of the bode plot aAND the pole zero plot. The bottom right is just the traditional pole zero digram (as would be seen from above on the 3D plot).