Graph help on Damping effects on SHM experiment

In summary, the conversation discusses an experiment involving a pendulum and its damping effect on a simple harmonic oscillator depending on the radius of the cardboard discs attached to it. The results showed a large spread between the time taken for the amplitude to diminish with varying disc sizes. The main confusion is how to plot a relationship between disc radius and time, with suggestions including plotting against the time taken for the angular displacement to reach 1 degree or fitting an equation to the data. The goal is to prove that as the disc radius increases, the damping effect also increases and potentially derive an equation for predicting the time for amplitude to decrease. New ideas include fitting an exponential function or calculating the damping coefficient.
  • #1
JamieGreggary
5
0
1. The problem

Okay. So just too briefly outline my experiment: I have a pendulum bob attached to two cardboard discs, and am testing to see how the radius of the cardboard discs effects the damping of the simple harmonic oscillator (the pendulum).

I have results (such as the one below which is off an 8cm diameter) ranging from 6cm to 22cm in diameter, producing a large spread of results between the time taken for the amplitude to diminish.

Now, what I am mainly confused about is how I could go about plotting a relationship between the circular disc radius, against time.

2. Relevant links

http://i50.tinypic.com/301oo6u.jpg

The Attempt at a Solution



I initially thought that I would just use the time taken for the pendulum to stop completely (i.e. have a 0 degree angular displacement), but this is too inaccurate as when the pendulum approaches 0, it starts to flicker between values and doesn’t stop completely.

I then thought that perhaps I could plot the circular disc radius against the time taken for the pendulum's angular displacement to reach 1 degree, as this is easy to find. However, it just sounds odd to have a set of results under "circular disc radius against the time taken for the pendulums angular displacement to diminish from 20 degrees (as this maximum the sensor can record) to 1 degrees". It doesn’t really tell us much, and wouldn’t really give us a concrete relationship to make predictions of pendulums amplitude after a time t with a circular disc of radius r.

4. Clarification
My main goal is to create a graph which will be able to quantifiably and graphically prove that as the radius of the circular disc increases, the damping effect increases. If possible, it would be nice to be able to derive an equation which allows us to make predictions of the time taken for the pendulums amplitude to decrease to say X when attached to circular discs of r.

Any ideas of what I could plot the circular disc radius against (it could even be completely different to what I have suggested)? Any help would be really appreciated!

Thank you very much! :-)

New ideas
Fit the equation y(t)=−(e^−at) * sin(ωt) to the graph, and plot the disc radius against the value of "a". Although, when fitting this to the data surely the accuracy of the function is going to be determined by the coordinate that you choose for the graph to pass through? (which I wouldn't be sure on which the optimum is)
Calculate the damping coefficient (or Q factor) - Although I'm not quite certain how you could do this from using the graph
 
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  • #2
The data suggests an amplitude modulation at about one third the dominant frequency. You could try taking a moving average of y-squared and fit an exponential to that.
 
  • #3
haruspex said:
The data suggests an amplitude modulation at about one third the dominant frequency. You could try taking a moving average of y-squared and fit an exponential to that.

Cheers for the response =]
 

FAQ: Graph help on Damping effects on SHM experiment

1. What is SHM and how is it related to damping effects?

SHM stands for Simple Harmonic Motion, which is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium. Damping effects occur when an external force, such as friction or air resistance, is applied to the system, causing the amplitude of the motion to decrease over time.

2. How do I plot a graph for a SHM experiment with damping effects?

To plot a graph for a SHM experiment with damping effects, you will need to measure the displacement of the system over time. The x-axis of the graph should represent time and the y-axis should represent displacement. Plot the data points and connect them with a smooth curve to represent the motion of the system over time. The amplitude of the curve will decrease as damping effects take place.

3. What is the equation for SHM with damping effects?

The equation for SHM with damping effects can be written as x = A * cos(ωt) * e^(-bt/2m), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, b is the damping coefficient, t is time, and m is the mass of the system.

4. How do I calculate the damping coefficient from my data?

The damping coefficient can be calculated by plotting a graph of ln(amplitude) vs. time. The slope of the line on this graph is equal to -b/2m, where b is the damping coefficient and m is the mass of the system. You can then solve for b by rearranging the equation.

5. How does damping affect the period of SHM?

Damping affects the period of SHM by increasing it. As damping effects decrease the amplitude of the motion, it takes longer for the system to complete one full cycle. This can be seen in a graph where the period is represented by the time it takes for the system to return to its starting point.

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