What do the symbols in the equation for a damped harmonic oscillator represent?

[JolleJ]

Hi there.

I'm having a problem explaining the physical meaning of the symbols in the equation for an underdamped Harmonic oscillator:

$$A*e^{k*t}*sin(w*t)$$

I can see that A is the amplitude of the first swing, which we will not see, since sin(w*t)=0 for t=0.
Now k is the damping constant and something, I don't what more to say about that.

The last one, w, I find the hard one. I cannot tell, what this is. I mean, it's not the angular velocity, since this is changing. It is some sort of frequency?

Likewise, when the oscillator is not damped, and the equation is:

$$A*sin(w*t)$$

What is the w here? Is the actual angualar speed here?
//EDIT:
Wait, I see that it cannot be angular speed here either, since this is of course also constantly changing, both in size and direction. I can't see, what it is. If someone could please exemplify it? Thanks. :)
//

Thanks in advance.

 

[mda]

It is an angular frequency (not velocity), describing the evolution of the phase of the oscillation... when w*t goes through 2pi the oscillation has gone through one cycle.
One cycle is one rotation in complex displacement space if we use the identity sin[wt]=Im[exp[i*w*t]]

 

[Astronuc]

$A*e^{k*t}*sin(\omega*t+\theta_o)$ would be the more general case where the sin($\theta_o$) at time, t=0, so that handles some initial displacement.

A good reference -

http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html

http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr.html

 

[JolleJ]

Thank you both very much!
However, I'm still having one problem. What is the period of the movement? I've heard that it's larger than for an undamped pendulum. Is this true? And also, is the period constant for a damped pendulum? I can't tell this from the equations, but some of you can maybe?

Thanks in advance.

 

[Cyrus]

What class is this for, physics I probably?

The period is T=2*pi/w [Hz]

Its the number of cycles each second of the body.

Your book should explain these things very clearly.

Keep asking questions and the math to your answers are going to get damn horrible real quick!