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    My teacher has set an experiment to do with pendulums. We basically have to make a pendulum with a time period of two seconds. We've been given the equasion
    t=2pi x sqrt(l/g) Where l is the length of the pendulum. So the time period is only dependent on the length of the pendulum. For a time period of 2 seconds I basically need a pendulum of length 1m.

    Then I need to find the damping constant of this pendulum, k, which exsists due to air resistance/ friction etc. They've given us the equation A=Be^-kn
    Where A is amplitude after n swings of the pendulum, B is the initial amplitude of the pendulum.

    So I need to measure A at different values of n, find a value of k for each instance (I'll measure to N=10 or so) and find an average). Then having fdund k, I will find which value of n makes A/B = 0.5, that is, for the initial amplitude to half, which is easy enough.

    I have two questions though, firstly, I've been told that when the amplitude has halfed, the pendulum will have lost 75% of its energy. Why is that?

    When I look on wikipedia, amplitude of a pendulum is measured as an angle, whereas I've been told to measure horizontal distance from the equilibrium position of the pendulum. Which is correct?

    I'm no good at practicals. I usually just do the practical to get an idea, and then make up my own results, since you're only markled on how you wrote up your results and explained them anyway. But in order to make my results, I need to give myself a value of k, and I'm not sure in what sort of area that should be in. Are we looking at numbers between 0 and 1, or larger than that?

    Thanks for any help , and sorry this might be the wrong forum, but it's help with the maths I'm looking for.
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    (Original post by jamie092)
    My teacher has set an experiment to do with pendulums. We basically have to make a pendulum with a time period of two seconds. We've been given the equasion
    t=2pi x sqrt(l/g) Where l is the length of the pendulum. So the time period is only dependent on the length of the pendulum. For a time period of 2 seconds I basically need a pendulum of length 1m.

    Then I need to find the damping constant of this pendulum, k, which exsists due to air resistance/ friction etc. They've given us the equation A=Be^-kn
    Where A is amplitude after n swings of the pendulum, B is the initial amplitude of the pendulum.

    So I need to measure A at different values of n, find a value of k for each instance (I'll measure to N=10 or so) and find an average).
    It is a way of doing this, but I'd recommend to present your experimental data in a graph. You can take logarithms of both sides of the equation A=B\exp \left( -kn \right) and plot \ln\left( B/A \right) versus number of swings n. Then you could draw the line of best fit and find its gradient, which is k. You can also easily work out the error in k this way.


    I have two questions though, firstly, I've been told that when the amplitude has halfed, the pendulum will have lost 75% of its energy. Why is that?
    You should already be familiar with this equation:

    x=A\cos \left( \omega t + \varphi \right).

    Differentiate it with regard to time to find velocity.

    Total energy = kinetic energy + potential energy. How does kinetic energy depend on velocity? Therefore, how does total energy depend on maximum velocity? How does it depend on amplitude?


    When I look on wikipedia, amplitude of a pendulum is measured as an angle, whereas I've been told to measure horizontal distance from the equilibrium position of the pendulum. Which is correct?
    Both, or to be precise, neither. Both methods use small angle approximation. Which means that as long as the greatest angle is not too great (let's say not greater than 5-7 degrees), you can use whichever method you prefer and you will get reliable results. Measuring horizontal distance will probably be easier than measuring angle.


    I'm no good at practicals. I usually just do the practical to get an idea, and then make up my own results, since you're only markled on how you wrote up your results and explained them anyway. But in order to make my results, I need to give myself a value of k, and I'm not sure in what sort of area that should be in. Are we looking at numbers between 0 and 1, or larger than that?

    Thanks for any help , and sorry this might be the wrong forum, but it's help with the maths I'm looking for.
    I have to disagree that making up one's own results is a good approach. In this case the value of k can be determined quite accurately and it will be difficult to guess the correct value.

    However, it's good to think what range of values you can expect before making measurements. I would expect k to be a rather small value - air resistance in this case is not too great. If k=1 that would mean that after each swing the amplitude would get 2.73 times smaller! It's surely less than that.
 
 
 
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