I mentioned critical damping as going into the dark places earlier in this thread because I could not think of an analogy that worked and the associated maths is horrible. However, this week I listened to the Gary Loomis podcast ( 20 Dec 2009) on the itinerant angler:
The Itinerant Angler
As well as being hugely entertaining it is very informative in a accessible way. He uses a great analogy of a diving board for a rod that allows me to explain damping. Please remember this only applies to the sprung portion of the cast.
We are looking to get the maximum energy from our rod (diving board) to the line (diver) by bouncing on the board (each end of cast). The board is clamped at one end by our hand.
If the diver cannot flex the board he cannot launch - underlined, rod too stiff, not enough acceleration in the cast - the system is under damped and operating near to natural frequency
A lot of energy is required to launch the diver becasue either the board flexes too much or the diver is of a generous girth - overlined, rod too soft, overpowered cast - the system is overdamped and the system is operating below natural frequency and is unresponsive.
The diver achieves a 1.5 somersault with pike - the line weight, rod stiffness and acceleration are all perfectly balanced - the system is operating at its resonant frequency
Hope it works for you