Q2 Hooke's law, which holds when a spring is not stretched too far, signifies that the extension of the spring and applied force are linearly related. The proportionality is parameterized by the spring constant $k$. A value for this parameter can be established experimentally by known weights onto the spring and measuring the resulting compression. Such data is contained in Table. Notice that above a weight of $40 \times 10^4$ N, the linear relationship between the force and displacement break down. Determine a value of $k$ for linear portion of this system. In addition, fit a non-linear relationship to the non-linear portion.
| Displacement, m | 0.10 | 0.17 | 0.27 | 0.35 | 0.39 | 0.42 | 0.43 | 0.44 |
|---|---|---|---|---|---|---|---|---|
| Force, $10^4$ N | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |
