Suppose we have the following setup, a mass on a spring attached to a wall, as shown in the diagram:
We are completely ignoring friction between the mass and the ground here, and we have an ideal spring too. The mass starts in the equilibrium position. Let's define a coordinate system such that the origin is the equilibrium position of the spring and the positive x axis to the right of the equilibrium point.
Let's now submerge this system in a fluid A, such that the motion of the mass is heavily over-damped (e.g molasses). We give the mass a kick to the right such that it has some initial velocity:
$$v = v_0$$ away from the wall.
Let's now submerge the system in a fluid B, so now the motion of the mass is critically damped. We give it the same initial velocity velocity away from the wall.
My question is, will the mass achieve a maximum displacement away from the equilibrium position (x=0) in fluid A or fluid B, or will the maximum displacements in each case be equal?