How Does Damping Affect the Amplitude of a Compound Pendulum?

[Brewer]

I have been given a question about damping that will form part of my A-level coursework, and I wondered if any of you could think of a decent way to go about it.

The brief is to investigate how the amplitude of a compound pendulum decreases with the degree of damping.

Equipment I will have access to:
Metre rule (to act as a pendulum)
Card (to be placed on the rule to damp the oscilations)
various measuring equipment

The initial thought that I had was to attach a piece of chalk to the pendulum, and touch it against a piece of paper/card to draw the oscilations so that I could accurately measure the amplitude of the oscilations and see the effect that damping had on the system as the area of the card was increased. However I soon realized that this would increase the friction in my system, therefore introducing more variables into my system (i.e it could be the friction of this and not the damping that reduces the amplitude of the oscilations).

My next idea was to see how to time differed for a set number of oscilations (10 for example). This is an idea that I may follow up and do some work with in my preliminary work.

Another idea on the "good" list would be to measure the amplitude of the oscilations and see how they differ. This is another possible idea, but again needs to be investigated in preliminary work. However I feel that it may be too difficult to accurately measure the amplitude, as its obviously not stationary when you need to measure it (well it is technically - just not for long!).

So could any of you give me some more ideas of how to go about this investigation, or suggest a relationship for this. I know it will involve a variable to the power of something, but I am unaware of where to start looking for this.

Thanks in advance for any help.

 

[Nate810]

One idea could be to measure the maximum angle of oscillation (theta) of the pendulum for a given unit of time (e.g. for 10 oscillations). This would allow you to measure the damping effect on the oscillations by comparing the maximum angle of oscillation before and after a given amount of damping. You could also measure the rate of change in theta (i.e. the angular acceleration) as well, which would give you an indication of how quickly the damping is affecting the pendulum's oscillations.

 

[wais]

One possible approach to investigate the effect of damping on the amplitude of a compound pendulum could be to use a photogate and light sensor system. This would eliminate the potential variable of friction in your system and allow you to accurately measure the amplitude as well as the period of oscillation.

You could set up the pendulum with a card attached to it, and place the photogate at a certain distance from the pendulum. As the pendulum swings, it will interrupt the light beam and the sensor will record the time it takes for the pendulum to complete one oscillation. You can then repeat this process for different degrees of damping (by varying the size of the card) and compare the periods of oscillation.

From this data, you can calculate the amplitude of the oscillations using the formula A = x0 - x1, where x0 is the maximum displacement and x1 is the minimum displacement. By plotting the amplitude against the degree of damping, you should be able to observe a decrease in amplitude as damping increases.

Another idea could be to use a high-speed camera to capture the motion of the pendulum and analyze the video to measure the amplitude. This would also eliminate the potential issue of friction and allow for more accurate measurements.

You could also investigate how different factors, such as the weight of the pendulum or the length of the string, affect the relationship between damping and amplitude. This could provide a more comprehensive understanding of the system.

In terms of finding a relationship, you could start by looking into the equation for damped harmonic motion, which takes into account the damping coefficient and the natural frequency of the pendulum. By manipulating this equation, you may be able to find a relationship between damping and amplitude.

Overall, there are many possible approaches and factors to consider in investigating the effect of damping on a compound pendulum. It's important to carefully plan and carry out your preliminary work to ensure accurate and reliable data, and to explore all possible avenues for your investigation. Good luck with your coursework!