A block of known mass \(m\) is placed on a rough, horizontal surface. One end of a light spring of unknown spring constant \(k\) is attached to the block, and the other end is attached to a fixed wall. The coefficient of kinetic friction between the block and the surface is \(\mu_k\). A student wants to determine the spring constant \(k\) by pulling the block to stretch the spring to various distances \(\Delta x\) from its equilibrium length, releasing the block from rest, and measuring its initial acceleration \(a\).

Assume that the initial acceleration \(a\) is measured immediately after the block begins to move, such that the frictional force acting on the block is the kinetic friction force \(f_k\).