Understanding Resonance and its Relationship to Frequency and Displacement

[svishal03]

Consider the attached xls which shows the plot between frequencies and resultant displacements.

Does resonance position always correspond to a point where the slope of the curve )curve between frequency and resultant displacement) is zero?

Please help

 

[Simon Bridge]

No.

The zero slope is a turning point, which may be a minima between two such peaks (eg where there is multiple resonance) or may just be part of the graph well away from the resonance depending on the situation.

 

[frankcastle50]

hi everyone i am new here and would like share my knowledge among you.

 

[Simon Bridge]

Welcome to PF - just "get posts" of the top bar and look for "no replies".

 

[svishal03]

What happens in a multiple resonance? Will there be multiple turning points?

What is the characterstic of resonance?

 

[Simon Bridge]

Resonance happens in driven oscillators, where the frequency of the driving function is close to the characteristic frequency of the oscillator. In a tunable radio circuit, you change the characteristic frequency of the oscillator (the circuit) against a background of EM radiation (the driving function) - we do this because radio stations strongly transmit in narrow ranges. If you plot the strength of the resulting signal against frequency you get that up-down pattern, with a peak everywhere there is a radio station.

There are other ways this can happen - for instance, we can supply a driving field to some structure in nature. The structure may respond resonantly to the field - for instance:

Resonant tunnelling is a QM phenomenon where a particle can escape a confining potential despite not having enough energy to "go over the wall".

... the vertical axis is the transmission coefficient and the horizontal is the energy (and thus the frequency) of the wave... as you'd expect, the higher the particle energy, the more likely it will get through the wall, so you get a general upward trend there. However, there are a bunch of sharp peaks appearing in the graph. These are the resonances. I count 7 of them.
... A resonance occurs where the width of the barrier is close to a half-integer multiple of the wavelength of the particle's wavefunction. It's like waves on a string - the resonances are the harmonics.

You can also get absorption resonances that appear as troughs instead of peaks.

Resonance is characterized by a strong narrow-bandwidth reaction to an applied field.