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Re: Forced damped pendulum



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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.
Fax (781) 647-1851 Weston, MA 02193

James,
What type of damping do you assume? If you have a damping force
proportional to the speed, it is a standard problem with an easily
available solution. If you deal with a CONSTANT damping force, i.e. a
constant force always in a direction opposite to the velocity, then it
becomes a fun problem to deal with. Can be done analyticlly too. Let me
know which it is you are dealing with.
Uri
Prof. Uri Ganiel
Learning by Redesign
Department of Physics
The Ohio State University
174 West 18th Avenue
Columbus, OH 43210-1106

Phone: (614) 292-0374
FAX: (614)292-3221

E-mail: GANIEL@pacific.mps.ohio-state.edu

(on leave from the Weizmann Institute of Science, Rehovot, Israel)






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<excerpt>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


<fixed>_ . . _ _ _ _ . . . _ . . . _ _

James A. Currie Weston High School

curriej@meol.mass.edu Science Department

Phone (781) 899-0620 x7146 444 Wellesley St.

Fax (781) 647-1851 Weston, MA 02193

</fixed>

</excerpt>James,

What type of damping do you assume? If you have a damping force
proportional to the speed, it is a standard problem with an easily
available solution. If you deal with a CONSTANT damping force, i.e. a
constant force always in a direction opposite to the velocity, then it
becomes a fun problem to deal with. Can be done analyticlly too. Let me
know which it is you are dealing with.

Uri

<fixed><bigger>Prof. Uri Ganiel

Learning by Redesign

Department of Physics

The Ohio State University

174 West 18th Avenue

Columbus, OH 43210-1106


Phone: (614) 292-0374

FAX: (614)292-3221


E-mail: GANIEL@pacific.mps.ohio-state.edu


(on leave from the Weizmann Institute of Science, Rehovot, Israel)





</bigger></fixed>

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