Re: Forced damped pendulum

[Sam Held <held@utkux.utcc.utk.edu>]

Jim,
	The easiest way to do this is using Lagrangians, that is the using
the Lagrnage function L=T-V (where T is kinetic energy and V is potential
energy).  Then the equation of motion is broken down into a simple diff
eq. d/dt(dL/domega)=dL/dtheta (if I remember correctly), where theta is
the angle of displacement from normal and omega is the time derivative of
theta (your time dependence).  

OR 

You can solve this using phase prtraits as well and the driven, damped
pendulum is a classic example.  I can get more info on this to you if you
wish.  However, I suggest this way because you don't leave Newtonian
mechanics but you learn about nonlinear differential equations which is
what the pendulum and spring systems are in real life (outside small angle
approximation and with frictional damping).  


							Sam Held

sheld@utk.edu


On Tue, 9 Jun 1998, James A. Currie wrote:

> I have a rather ambitious student who,  for a Senior project,  is attempting to
> analyze the motion of a driven damped pendulum.  We have gone through the more
> simple case of a mass on a spring found in most texts.
>
> He has developed a 2nd order differential (using Newton's 2nd law) to describe the
> motion and is now attempting to solve it.  Does anyone have any ideas for arriving
> at a mathematical expression for the pendulum's angular displacement as a function
> of time?  (I have plenty of ideas,  but won't bore you with the details ... yet.)
>
> - Jim
>
>
> _ . . _ _ _ _ . . . _ . . . _ _
> James A. Currie             Weston High School
> curriej@meol.mass.edu       Science Department
> Phone (781) 899-0620 x7146  444 Wellesley St.
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