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Hooke's Law model

This document describes the model for the Hooke's Law simulation.
@author Chris Malley (PixelZoom, Inc.)

Single Spring

For a single spring, or a system treated as a single "equivalent" spring:

F = kx
E = kx2 / 2

where:

  • F = applied force, N
  • k = spring constant, N/m
  • x = displacement from equilibrium position, m
  • E = potential energy, J

Series Springs

For 2 springs in series:

Feq = F1 = F2
keq = 1 / ( 1/k1 + 1/k2 )
xeq = x1 + x2
Eeq = E1 + E2

where:

  • subscript "eq" pertains to a spring that is equivalent to the 2 springs in series
  • subscript "1" pertains to the left spring in this sim
  • subscript "2" pertains to the right spring in this sim

Parallel Springs

For 2 springs in parallel:

Feq = F1 + F2
keq = k1 + k2
xeq = x1 = x2
Eeq = E1 + E2

where:

  • subscript "eq" pertains to a spring that is equivalent to the 2 springs in parallel
  • subscript "1" pertains to the top spring in this sim
  • subscript "2" pertains to the bottom spring in this sim