Here is your problem, self-proclaimed relativity expert:

   k       m
/\/\/\/\---O

m is rest mass and k is a linear spring, massless in this case. The
free end of the spring is atatched to a locally inertial frame a

For example, in Newtonian mechanics, the equations are derived in one
line as follows (for non-relativistic cases): F = dp/dt = -kx, in the
case of an unforced oscillator the equation of motion is: md^2x/dt^2+kx
= 0, x(t=0) = x0, dx/dt(t=0) = v0

Go ahead and write down the relativistic equation of motion according
to GR. Assume v0/c = 0.9.  Don't scream, shout or throw curses as
usual. Hint: avoid just stating G = T.

Come on Dork, show us what kind of expert you are. I will not ask you
to solve the equations now. Maybe later.

You are allowed to ask for help from other cranks in these groups,
including your local priest, etc.

NOTE: DO NOT BY ANY MEANS REFER TO NEWTON.

Mike