<Dl> <Dd> T = 2 π m k . (\ displaystyle T = 2 \ pi (\ sqrt (\ frac (m) (k))).) </Dd> </Dl> <Dd> T = 2 π m k . (\ displaystyle T = 2 \ pi (\ sqrt (\ frac (m) (k))).) </Dd> <P> 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). </P> <P> Substituting ω with k / m, the kinetic energy K of the system at time t is </P>

Lagrangian equation of harmonic motion of spring mass system