Question

Describe the young quasimodo

Answer 1

Answer:

A familiar example is the perturbation (gentle tap) of a wine glass with a knife: the glass begins to ring, it rings with a set, or superposition, of its natural frequencies — its modes of sonic energy dissipation. One could call these modes normal if the glass went on ringing forever. Here the amplitude of oscillation decays in time, so we call its modes quasi-normal. To a high degree of accuracy, quasinormal ringing can be approximated by

{\displaystyle \psi (t)\approx e^{-\omega ^{\prime \prime }t}\cos \omega ^{\prime }t}\psi (t)\approx e^{{-\omega ^{{\prime \prime }}t}}\cos \omega ^{{\prime }}t

where {\displaystyle \psi \left(t\right)}\psi \left(t\right) is the amplitude of oscillation, {\displaystyle \omega ^{\prime }}\omega ^{{\prime }} is the frequency, and {\displaystyle \omega ^{\prime \prime }}\omega ^{{\prime \prime }} is the decay rate. The quasinormal frequency is described by two numbers,

{\displaystyle \omega =\left(\omega ^{\prime },\omega ^{\prime \prime }\right)}\omega =\left(\omega ^{{\prime }},\omega ^{{\prime \prime }}\right)

or, more compactly

{\displaystyle \psi \left(t\right)\approx \operatorname {Re} (e^{i\omega t})}\psi \left(t\right)\approx \operatorname {Re}(e^{{i\omega t}})

{\displaystyle \omega =\omega ^{\prime }+i\omega ^{\prime \prime }}\omega =\omega ^{{\prime }}+i\omega ^{{\prime \prime }}

Here, {\displaystyle \mathbf {\omega } }\mathbf {\omega } is what is commonly referred to as the quasinormal mode frequency. It is a complex number with two pieces of information: real part is the temporal oscillation; imaginary part is the temporal, exponential decay