How to Plot Amplitude of a Driven Oscillator with Damping?

[w3390]

Homework Statement

The oscillator is driven by a force F(t) = mAcos(wt). Plot the amplitude D of oscillations, in units of the maximum (resonant) amplitude D(max), as a function of w in units of w_0. (In other words, plot D/D(max) versus w/w_0.) Find Q.

$$\beta$$=(1/6)w_0

Homework Equations

D = A/[sqrt((w_0^2 - w^2)^2 + 4w^2$$\beta$$^2)]

A = (F_0)/m

The Attempt at a Solution

To start off, is my equation for D correct?

If so, my next question is how do I begin this problem. Is it correct to plug in (1/6)w_0 for the beta in my D equation to get D(max). That way I can divide D by D(max) and get the first part. Or is that completely wrong?

Any help would be greatly appreciated.

 

[anathema]

Thank you for your post. Your equation for D is correct. To begin this problem, you can start by plotting D/D(max) versus w/w_0, as mentioned in the homework statement. This will give you a plot of the amplitude as a function of w, normalized by the maximum amplitude at resonance.

To find Q, you can use the formula Q = w_0/2\beta. In this case, since you have been given \beta = (1/6)w_0, you can plug this into the formula to get Q = 3. This value of Q represents the quality factor of the oscillator, which is a measure of how well the oscillator maintains its amplitude over time.

I hope this helps. Please let me know if you have any further questions.