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# Total energy of SHM

The potential energy $(E_{\text{p}})$ and kinetic energy $(E_{\text{k}})$ of an object undergoing simple harmonic motion vary in an opposing fashion.

When the potential energy of the object is maximal, its kinetic energy is minimal and when its kinetic energy is maximal, its potential energy is minimal.

The object has maximum kinetic energy at maximum velocity (which occurs at the equilibrium point) and zero kinetic energy when its velocity is zero (which occurs at the amplitudes).

Similarly, the object has maximum potential energy at minimum velocity and minimum potential energy at maximum velocity.

The total energy $(E_{\text{T}}=E_{\text{k}}+E_{\text{p}})$ of an object undergoing simple harmonic motion is given by:$$E=\frac{1}{2}m\omega^{2}x_{0}^{2}$$The total energy of the system is thus conserved (i.e. the system is closed). The total energy is equivalent to the maximum kinetic or potential energy of the object.