Power of a thrust to maintain an extended spring
I have a question about working out the power to maintain equilibrium with a spring:
I attach a rocket to a horizontal spring and fire the rocket horizontally. This is done on a track or something similar. The spring will extend until the tension in the spring equals the thrust of the rocket (assuming the thrust is constant) at which point the system will be in equilibrium.
The rocket is clearly doing work to maintain this situation, but how do I calculate this work?
W=Fx doesn't seem right as nothing is moving any distance. While the spring was extending the rocket was putting work in to it equal to 1/2 Kx^2, but I'm not interested in that. I want to know the power required to maintain the equilibrium.