**Time response of RC+R circuit to single sinusoidal pulse (2: piecewise) [MOVED]

This video obtains the time response of a circuit with 2 resistors and 1 capacitor when subject to a a sinusoidal pulse (half-period) and non-zero initial conditions.
The approach to the problem and the summary of the aforementioned video are outlined in the first 2.5 minutes of this material.

Here, the same problem is solved in a ``piecewise'' manner, dispensing with the concepts of {delay} and {superposition} of the video referred to above.
Two main concepts are used:

--Causality: if the single pulse and the full sine coincide during the first 0.01 seconds, their outputs will also coincide in that interval (the output does not depend on future changes in the input waveform).
--The concept of "state": all the past is summarized in the state (capacitor charge) at the moment when the input stops being sinusoidal.

These two ideas allow us to solve two differential equation problems, one for the interval [0,0.01] and another for t greater than 0.01, with the initial condition of the second interval being equal to the ``final'' condition of the first.

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#matlab #electricalengineering #laplace #controlengineering
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Antonio Sala
Universitat Politècnica de València

[robertooconlara]

Another excellent video mr. Salas, i have been working so i haven't seen your recent work. I can't imagine the days when all of this was done by hand, have you ever worked the equations used by the NASA when they launch rockets? there are pictures of thousands of pages of code and maths, I remember something about the mass and the power needed by every phase, when it discard the tank, something about the trajectory, in satellites and to the moon, I hope it results useful for your channel