Resonance

Thread Starter

TAKYMOUNIR

Joined Jun 23, 2008
352
why at resonance the output signal is sinusoidal and this does not depend on the input signal (I mean the input signal could be square,triangle ,or any waveform) and at resonance the output is sinusoidal
 

MikeML

Joined Oct 2, 2009
5,444
You are making it too complicated.

Think of a physical analogy. Put a child on a swing. Push child with short sudden motions (square wave drive). Swing motion is smooth and sinosoidal in spite of short pushes...

Go back to Wiki and search for Q in the context of resonance.
 

MaxHeadRoom

Joined Jul 18, 2013
19,074
Also think of the audio analogy when a bell is struck or a blast of air is sent down a pipe, both will produce a resonant sinusoidal audio wave.
Max.
 

studiot

Joined Nov 9, 2007
5,002
why at resonance the output signal is sinusoidal and this does not depend on the input signal (I mean the input signal could be square,triangle ,or any waveform) and at resonance the output is sinusoidal

can we say because the resonance happen at on harmonic(one frequency) that is why the signal is sinusoidal because any signal according to fourier series is acombination of harmonics
The second statement is better since resonance is a function of the frequency of the input waveform (= the forcing function), not its waveshape.

The point is that the system response is generated not by the forcing fucntion but by the circuit characteristics.
So , as Max said, if you excite (give it energy) an oscillator it oscillates and generates a new signal by its own action.
So there are then two signals present, the original signal and the newly generated signal.
It is their combination that determines the composite result.
If the frequency of the forcing function exactly matches that of the newly generated signal they will reinforce and resonance occurs.
If they mismatch then some parts of the waveforms will reinforce and some will interfere destructively, reducing the output.

When you write the circuit equations involving inductance and/or capacitance they are differential equations.
These differential equations (can you do these?) have two part solutions that reflect the above explanation, as in MikeML's link.
The newly generated wave solution is sinusoidal.
 
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