# Lagrangian [Lagrangian](Lagrangian.md) # Hamiltonian Absent of external forces, the Harmonic oscillator [Hamiltonians](Hamiltonians.md) model [a conserved energy](Conserved%20quantity.md) and thus give the total [energy](Mechanics%20(index).md#Energy) of the system. ^0c15d6 # As an approximation The _Harmonic Oscillator_ is a useful approximation of any perturbation close to a local minima in any [smooth](Smooth%20function.md) potential function. #Mechanics #Mechanics/WaveMechanics #Mechanics/ClassicalFields #PhysicalExamples/PhysicalExamplesInMechanics