Understanding Forced Damped Oscillations at Resonance and Low Frequencies

[astrozilla]

Homework Statement

At the natural frequency,ω0 what are the real and imaginary components of Avel(ω) ?

Sketch a phasor diagram with the velocity vector and driving force vector,and use this to provide the phase difference between Avel(ω) and the driving force if ω=ω0 (ι.e at resonance),

and in case ω<<ω0,state whether the velocity leads or lags the driving force

Homework Equations

Avel(ω)=(F0 iω )/[m (ω^2 -ω0^2 +iγω)] where γ=b/m

The Attempt at a Solution

in the first case where ω=ω0 ,maybe the imaginary part of Αvel(ω) is zero since ,Avel(ω)=F0/mω^2 =F0/k

 

[nickjer]

What is Avel? Also, to get more responses it is best to use latex when posting equations.

I also don't completely agree with your answer at the end. When I plug in w_0 into your equation, I still retain the damping constant \gamma.

 

[astrozilla]

Avelocity is the Amplitude response to velocity,
What do you mean latex ?

 

[nickjer]

Then you solved for A_{vel}(w_0) wrong. Latex is a format that makes equations look cleaner. You use the format "tex" with brackets replacing the quotations. You can usually google the latex commands for symbols. One trick is to click on the equations people posted already and a window appears with the commands they used.

 

[astrozilla]

Thanks for the advise,
as i become more educated i will use more latex !