Chapter 1, Problem 1.15P

The distance a spring stretches from its “free length” is a function of how much tension is applied to it. The following table gives the spring length y that was produced in a particular spring by the given applied force f. The spring’s free length is 4.7 in. Find a functional relation between f and x, the extension from the free length (y = y − 4.7).

$\begin{array}{l}\underset{¯}{\text{Force }f\left(\text{pounds}\right)}\\ 0\\ 0.47\\ 1.15\\ 1.64\end{array}$ $\begin{array}{l}\underset{¯}{\text{Spring length }y\left(\text{inches}\right)}\\ 4.7\\ 7.2\\ 10.6\\ 12.9\end{array}$