Free vibrations of any elastic body is called natural vibration and happens at a frequency called natural frequency. Natural vibrations are different from forced vibration which happen at frequency of applied force (forced frequency). If forced frequency is equal to the natural frequency, the amplitude of vibration increases manifold. This phenomenon is known as resonance.
In electrical circuits, s1 is a natural frequency of variable x, if the zero-input response of x includes the term where is a constant dependent on initial state of the circuit, network topology, and element values. 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. Natural frequencies depend only on network topology and element values but not the input. 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. 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.
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