Mass on a Spring

Hooke's Law

the spring pulls back

A spring pushes back toward its resting position with a force proportional to how far it is stretched or squashed.

Example

A spring pushes back toward its resting position with a force proportional to how far it is stretched or squashed.

highlighted = computed this step

The spring pulls back in proportion to the stretch

Stretch or squash a spring and it pushes back toward its resting position. The restoring force is the stiffness times the displacement, and the minus sign just means it always points back toward the middle. Stretch twice as far and it pulls twice as hard.

F=−k xF = -k\,x
A stretched spring pulls the block backA block pulled to the right, stretching the spring, with a restoring force arrow pointing back toward the middle.mF

A worked value

With stiffness 2 newtons per metre, pulling the block out to 3 metres gives a restoring force of 2 times 3, or 6 newtons, pointing back toward the middle.

F=k x=2 N/m ⋅ 3 m=6 NF = k\,x = 2\ \text{N/m} \,\cdot\, 3\ \text{m} = \hl{6}\ \text{N}
mechanics A 2 N/m spring pulled to 3 m gives a clean 6 N restoring force.