Mass-Spring system on an accelerating jet

The acceleration of the plane will cause an offset in the motion of the mass/spring system; if it was centered on x=0 when the plane was stationary, its motion will now be centered around $x = -frac{mcdot a}{k}$ where $k$ is the spring constant, and $F = mcdot a$ is the force needed for the mass to accelerate with the plane. If the plane is accelerating in the +x direction, the displacement will be in the -x direction.

Apart from that there is no change - not to the frequency, not to the damping.