:where : Since ω = 2πf,: and, since where T is the time period, : These equations demonstrate that the simple harmonic motion is

*isochronous*(the period and frequency are independent of the amplitude and the initial phase of the motion). Substituting ω 2 with k⁄m, the kinetic energy K of the system at time t is :and the potential energy is :In the absence of friction and other energy loss, the total mechanical energy has a constant value : The following physical systems are some examples of simple harmonic oscillator. A mass m attached to a*spring*of*spring*constant k exhibits simple harmonic motion in closed space.