Mechanical Oscillators
SHM, DHM, SHO, and DHO refer to simple harmonic motion, damped harmonic motion, simple harmonic oscillator and damped harmonic oscillator respectively.
Physical situation  Nomenclature  Translational equations  Angular equations 

SHM 

Solution: 
Solution: 
Unforced DHM 

Solution (see below for ω'): Resonant frequency: Damping rate: Expected lifetime of excitation: 
Solution: Resonant frequency: Damping rate: Expected lifetime of excitation: 
Physical situation  Nomenclature  Equations 

Linear undamped unforced SHO 


Linear unforced DHO 


Low amplitude angular SHO 


Low amplitude simple pendulum 

Approximate value Exact value can be shown to be: 
Physical situation  Nomenclature  Equations 

SHM energy 

Potential energy Maximum value at x = A: Kinetic energy Total energy 
DHM energy 
Read more about this topic: Linearrotational Analogs
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