Dampening effect on a pendulum

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To calculate the time it takes for a pendulum to come to a complete stop due to damping effects, one must consider the damping forces, including friction at the pivot and air resistance. The time period formula T=2π√(L/g) is useful for determining the swing period, but it does not account for damping. The total time until the pendulum comes to rest cannot be calculated without knowing the specific damping coefficients. Experimental determination of these coefficients is necessary to apply the appropriate equations for damping. Understanding these factors is crucial for accurately modeling the pendulum's motion and decay.
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Ok, my mind has gone blank. What equation do I use to calculate the time a pendulum will take to come to a complete stop?.. I have all variables, length of string, angle it was released, etc.. I know the equation for period, but how do I figure how long till it stops from DAMPENING effect..?

This isn't really a homework question, its just for something I am building. So hopefully this is the right place to post. Thanks!
 
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I guess you use the time period formula for pendulum
T=2pie.sqrt(L/g)
 
That would vary from pendulum to pendulum... there's no way to calculate how long it keep swinging without knowing the sources of friction. There's friction 1. in the bearing of the pendulum's pivot point (unless its a wire tied to a point, in which case there's energy lost in the wire) 2. between the surface of the pendulum's weight or 'bob' and any gas or liquid it's swinging in.

Once you know that damping force (experiment) you can use the equation here: http://en.wikipedia.org/wiki/Pendulum
 
Ok, so, forgive me if these questions are remedial, physics is not my strongest subject. So: If, knowing the total coeffeicient of friction (of the pivot point, as well as the air resistance) what equation would represent total time until the pendulum comes to rest?
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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