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Pendulum Damping with concentration on Frictional Forces according to Angular Velocities

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by

Sarah Drum

on 17 May 2010

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Transcript of Pendulum Damping with concentration on Frictional Forces according to Angular Velocities

Pendulum Damping with Concentration on Frictional Forces according to Angular Velocities by Joshua Godwin
Discussion Topics Simple Pendulum Damping Pendulum The Equation The Mathematical Properties
of the Equation Comparisons of Frictional Forces with
Respect to their Velocities A Simple Pendulum is a concept and does not really exist in nature.
A Simple Pendulum has a massless cord and
is suspended from a pivot without friction.
A Simple Pendulum also has a constant Amplitude, this is
because the pendulum has no air drag.
A Damping Pendulum is what truly happens in nature. Damping is an approximation to the friction caused by drag. With damping, the pendulum will
eventually come to rest according
to the velocity and drag.
The equation I used is exactly like the
simple pendulum equation, but with
a frictional constant added on.
The initial conditions are displayed in the braces.
I chose the velocities that are used for the reason of having a velocity lower than 1. I used a value larger than 1, 2.5. As well as a value higher than 2.5, 6.
The graph on the left has a frictional constant of 0.626 and a velocity of 2.5.
The graph on the right has a frictional constant of 0.626 and a velocity of 6.
The graph at the bottom has a frictional constant of 0.626 and a velocity of 0.5.
Do you see any changes in the graphs?
The graph on the left has a frictional constant of 0.5 and a velocity of 2.5.
The graph on the right has a frictional constant of 0.5 and a velocity of 6.
The graph at the bottom has a frictional constant of 0.5 and a velocity of 0.5.
Do you see any changes in the graphs?
The graph on the left has a frictional constant of 0.1 and a velocity of 2.5.
The graph on the right has a frictional constant of 0.1 and a velocity of 6.
Do you see any changes in the graphs?
The graph on the left has a frictional constant of 1 and a velocity of 2.5.
The graph on the right has a frictional constant of 1 and a velocity of 6.
The graph at the bottom has a frictional constant of 1 and a velocity of 0.5.
Do you see any changes in the graphs?
The graph on the left has a frictional constant of 1.5 and a velocity of 2.5.
The graph on the right has a frictional constant of 1.5 and a velocity of 6.
The graph at the bottom has a frictional constant of 1.5 and a velocity of 0.5.
Do you see any changes in the graphs?
Now I will be changing the frictional constant to match the velocity of 2.5
Describe some characteristics of the graph?
Velocity of 6.
What are some obvious characteristics of this graph?
Velocity of 2.5
What are some changes when the friction is larger than the velocity?
Velocity of 6
What are some obvious
characteristics of this graph?
Velocity of 2.5 and 6
What if I had negative friction? Velocities of 2.5, 6 and 0.5
What do you think will happen if I had no friction? Conclusion Through this research, I discovered that the 3 angular velocities were not effected by the lower frictional forces.

The major changes that occurred were when the frictional forces were larger than the angular velocities.

With the lower velocities and slightly higher frictional forces the pendulum was still able to swing before coming to rest.
But with the higher velocity and slightly higher frictional force the pendulum just gradually came to a stop.

I believe this just has to do with the frictional force. No matter what the velocity. The more frictional force, the faster the pendulum will stop, even if the pendulum never gets to swing.
Questions? Questions?
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