# Natural frequency

In electrical circuits, s1 is a natural frequency of variable x, if the zero-input response of x includes the term $K_{1}e^{-s_{1}t}$ where $K_{1}\neq 0$ is a constant dependent on initial state of the circuit, network topology, and element values.Template:Sfn In a network, sk is a natural frequency of the network if it is a natural frequency of some voltage or current in the network.Template:Sfn Natural frequencies depend only on network topology and element values but not the input.Template:Sfn It can be shown that the set of natural frequencies in a network can be obtained by calculating the poles of all impedance and admittance functions of the network.Template:Sfn All poles of the network transfer function are also natural frequency of the corresponding response variable, however there may exist some natural frequencies that are not a pole of the network function, these frequencies happen at some special initial states.Template:Sfn
$\omega _{0}={\frac {1}{\sqrt {LC}}}$ 