An electric circuit is described by the following equation: d’u du +k- +w³u = au° , dt? dt where t is time in seconds, and @, k, and a are positive constant parameters. a)Present this equation in the form of the energy balance equation. Find the total instantaneous energy of the circuit E and the dissipative function F. b)Present a sketch of the effective potential energy of the circuit as the function of voltage u;

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An electric circuit is described by the following equation:
d’u
du
+k+o°u = au,
dt
dt?
where t is time in seconds, and @, k, and a are positive constant parameters.
a)Present this equation in the form of the energy balance equation. Find the
total instantaneous energy of the circuit E and the dissipative function F.
b)Present a sketch of the effective potential energy of the circuit as the
function of voltage u;
- find the points of equilibria; and
- determine their character (whether they are stable or unstable?).
Transcribed Image Text:An electric circuit is described by the following equation: d’u du +k+o°u = au, dt dt? where t is time in seconds, and @, k, and a are positive constant parameters. a)Present this equation in the form of the energy balance equation. Find the total instantaneous energy of the circuit E and the dissipative function F. b)Present a sketch of the effective potential energy of the circuit as the function of voltage u; - find the points of equilibria; and - determine their character (whether they are stable or unstable?).
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