For a physics laboratory assignment, one end of a spring is attached to a horizontal rod so that the spring hangs vertically, and a ruler is hung vertically alongside the spring. The stretching properties of the spring are to be measured by attaching eight identical beads to the spring's free end. With no beads attached, the free end of the spring is at a ruler reading of \(23.4 \mathrm{~mm}\). With one bead attached, the end of the spring drops to \(25.2 \mathrm{~mm}\). When the second, third, and fourth beads are attached one at a time, the end drops to ruler readings of \(26.5 \mathrm{~mm}, 29.1 \mathrm{~mm}\), and \(30.8 \mathrm{~mm}\), respectively. Adding the fifth and sixth beads together moves the spring end to \(34.3 \mathrm{~mm}\), and adding the last two beads moves the end to \(38.2 \mathrm{~mm}\).

(a) Make a pictorial representation of this setup.

(b) Tabulate the data.

(c) Plot the data on a graph, showing the ruler readings on the vertical axis and the numbers of beads on the horizontal axis.

(d) Describe what can be inferred from the data.