I am asked to rate a series of elastic collisions in order of greatest time of max compression to least time of max compression for several vehicles with varying masses and velocities, which strike a spring with a spring constant k.
I can determine the Momentum of each case, as I am given the masses and velocities. Additionally, I can determine each of their kinetic energy.
I know that the kinetic energy of the car will be converted into potential energy in the spring:
Also, I know the impulse of the car's is going to be
$$Ft= Δvm $$ $$ t=Δvm/F$$
I also know that the Force on spring will be $F=kx$, but I am not sure how the magnitude of the momentum of the cars' is going to relate to the time of maximum spring compression. I am asking for a little guidance in my reasoning.