Physics of tidal locking: can the process be underdamped? Is it possible for a satellite undergoing the process to overshoot the required rotation rate for tidal locking?   For example, if its rotation rate is being slowed, can it become slower than it needs for tidal locking and then oscillate back as it is torqued the other way?   If it can happen, how long can such an oscillation persist?
 A: As far as I understand the phenomenon (and it's a little outside my wheelhouse, so I may be putting my foot in my mouth), tidal locking is entirely a result of damping - the fluid friction and solid stresses that convert rotational energy into heat because of the gradient in gravitational field strength.
So, if you take away the damping, there's no effect at all - there would be no slowing of the rotation rate.  If you reduce the damping (by making the satellite stiffer, or moving it further away from the parent, etc), it would just tidally lock more slowly.
A linear analogy would be a book sliding across the floor and coming to a stop.  You wouldn't think that if you took away the friction, it might overshoot that spot then come back.
A: I guess it depends on what you mean by "oscillate back".  I believe that we were thinking of different things here.
A better analogy might be a vertical circular pendulum (one that is free to go all the way around).  If we give the pendulum a lot of energy, it will rotate all the way around the axis.  If there is friction, then the pendulum will eventually not have enough energy to make it over the top and it will swing back and forth at the bottom. 
A planet becoming tidally locked will behave similarly.  
When you mentioned "oscillate back faster", I imagined you meant that it might rotate around in the other direction (completely) or pick up speed in the other direction.  It won't do that.  It will oscillate with decreasing amplitude.  If that's the oscillation you mean, then yes it can, and with minimal damping it can persist indefinitely (like a minimally damped pendulum).
