Effect of spring on dynamic load

[GunnaSix]

Homework Statement

A prismatic bar (with flange on bottom) has length L, diameter d (so A=(pi/4)d^2), and modulus of elasticity E. A spring of stiffness k is installed at the bottom of the bar (on top of flange). A sliding collar of mass m drops from a height h (above the top of the spring) onto the spring. Determine the maximum elongation delta_max of the bar. Assume no energy losses and disregard the masses of the spring, flange, and bar.

2. The attempt at a solution

It seems to me like this system is really just equivalent to two springs in series (the bar could be considered to be in compression under the spring, and the analysis would be the same). We can find k_bar = E*A/L. I'm stuck here though. How do the two springs react to the dynamic load? At equilibrium we will end up with delta_bar/delta_spring=k_spring/k_bar, but my intuition tells me that isn't what's going on dynamically.

 

[Valkarie]

I think I should use the kinetic energy of the mass at the instant it hits the spring, but I'm not sure how to plug that into an equation.