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Math Help - Pit and Pendulum problem

  1. #1
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    Pit and Pendulum problem

    A simple pendulum consists of a lead bead hanging from a fixed point atthe end
    of a string of length L(metres). When the bead is moved slightly to one side and
    then released, it will swing to and fro. The time taken for the bead toperform a
    complete oscillation (i.e. to return to its starting point) is known asthe period, T
    (seconds).



    A group of students perform an experiment, timing small oscillations ofsuch a
    simple pendulum, and obtain the following data.

    Length L (metres) 0.6 0.7 0.8 0.9 1.0
    Period T (seconds) 1.55 1.68 1.79 1.90 2.01

    (a) Thispart of the question asks you to find a relationship of the form T = aLbbetween L and T.
    Enter the data into your spreadsheet, and use apower regression facilities to find the regression equation.

    (i) Write down the values of a, b and r (the correlation coefficient) given bythe calculator or spreadsheet.
    (ii) Write down the equation for T in terms of L,expressing the constants to
    2 decimal places.
    (iii) Imagine that you are in the group ofstudents collecting the data. Explain,
    as if to a fellowstudent, two difficulties which you would anticipate
    in collectingaccurate data.




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  2. #2
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    Re: Pit and Pendulum problem

    Quote Originally Posted by Magical View Post
    A simple pendulum consists of a lead bead hanging from a fixed point atthe end
    of a string of length L(metres). When the bead is moved slightly to one side and
    then released, it will swing to and fro. The time taken for the bead toperform a
    complete oscillation (i.e. to return to its starting point) is known asthe period, T
    (seconds).



    A group of students perform an experiment, timing small oscillations ofsuch a
    simple pendulum, and obtain the following data.

    Length L (metres) 0.6 0.7 0.8 0.9 1.0
    Period T (seconds) 1.55 1.68 1.79 1.90 2.01

    (a) Thispart of the question asks you to find a relationship of the form T = aLbbetween L and T.
    Enter the data into your spreadsheet, and use apower regression facilities to find the regression equation.

    (i) Write down the values of a, b and r (the correlation coefficient) given bythe calculator or spreadsheet.
    (ii) Write down the equation for T in terms of L,expressing the constants to
    2 decimal places.
    (iii) Imagine that you are in the group ofstudents collecting the data. Explain,
    as if to a fellowstudent, two difficulties which you would anticipate
    in collectingaccurate data.




    Seems a bit odd that you would model oscillation with an exponential function instead of trigonometric...
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  3. #3
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    Re: Pit and Pendulum problem

    how would u have modelled it?
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  4. #4
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    Re: Pit and Pendulum problem

    Well since I know that it's oscillating, I would have used a sine curve...
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  5. #5
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    Re: Pit and Pendulum problem

    how would u have used the sine curve
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