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Second Order ODE and RLC Circuit - Coggle Diagram
Second Order ODE and RLC Circuit
RLC Circuit
Definition
An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel
The circuit forms a harmonic oscillator for current, and resonates in a manner similar to an LC circuit.
We can combine R, L and C into differenties topologies.
Topology = Form taken by the network of interconnections of the circuit components.
Second Order ODE
Definition
Ordinary differential equation in which any derivatives with respect to the independent variable have order no greater than 2.
An equation involving the unknown function y, its derivatives y' and y'', and the variable x.
Notations
Initial condition
The second order equation needs two initial values, normally there values are y(0) and y'(0).
Applications of second order ODE
Differential geometry
Autoparallel curves
Geodesiscs of the Riemann and Finsler geometries
integral curves of the Reeb field on a contact manifold
Classical mechanics
Newton's equations of motion
Euler-Lagrange equations of a mechanical Lagrangian
General relativity
Worldlines of free particles
Classical electrodynamics
Describe the paths of charged particles.
RLC circuits applications
Oscillator circuits
Eletronic circuits that produces a periodic oscillating signal.
It is also used to select a frequency range different from ambient radio waves in radio receivers and television sets.
Band-pass filter
It's a device such that passes frequencies in a certain range and rejects a frequency if it's outside the range
Band-stop filter
Filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels
