Harmonic Oscillators: Resonance Bandwidth & Frequency Range

[fifteenover4]

Show that the resonance bandwidth corresponds to the frequency range for
which –1 < tan χ < +1. (The resonance bandwidth is the range for which the
average power is greater than 0.5 times the peak power.)

I'm pretty damn stumped with this.

 

[BvU]

Hello 4:15,
Could you use the template so that others know what this is about?
And that they can also see what $\chi$ stands for ?
And what you already know about these peak and average powers ?

 

[fifteenover4]

I've re-written it exactly as it was handed to me, hence, being stumped.

We know nothing about the peak and average powers, Ki is, I assume the impedance angle.

 

[BvU]

Hello again. Still wondering if this is mechanics or electronics. Never mind, some things are universal. Google "forced harmonic oscillator" or "forced harmonic oscillator solution" to get going.

I don't feel like re-hashing the formulas. They are ubiquitous, e.g http://www.physics.oregonstate.edu/~tate/COURSES/ph421/lectures/L9.pdf (Prof. J Tate), UTexas (prof. R. Fitzpatrick), etc. etc.
Basically what you should have collected under 2. of the template.

Being stumped when confronted with something new (? isn't this in some curriculum context?) isn't good enough. Do something and get stuck somewhere; then describe the situation you are in and ask for help. You are not being helped at all if someone else does that for you. Read the guidelines.

Once you have understood the derivation and the expressions (the investment is well worth it; lasts you a lifetime) it is a piece of cake to show what is asked of you.

All this is well meant and certainly not intended offensively.