3.4.1—Hooke's law

For a spring or elastic string obeying Hooke’s law, the tension or compression is proportional to extension or compression: F=λx/l, where λ is the modulus of elasticity and l is the natural length.

The model applies only within the elastic range and uses extension from the natural length, not the total length. Work done is the area under the force–extension graph.

If λ/l=50 N m⁻¹ and extension is 0.04 m, the force is 2.0 N; the elastic energy is ½Fx=0.040 J.

Returning to the original length does not prove Hooke’s law held throughout, and compression/extension signs must match the chosen convention.