# Forced Damped Oscillations

1. May 10, 2010

### astrozilla

1. The problem statement, all variables and given/known data
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

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

3. 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

2. May 10, 2010

### 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 $\gamma$.

3. May 10, 2010

### astrozilla

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

4. May 10, 2010

### 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.

5. May 10, 2010