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Math Help - Calculus - Error

  1. #1
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    Calculus - Error

    The time of oscillation, T seconds, of a simple pendulum is very nearly equal to 2/L , where L is the length of the pendulum in metres. A pendulum is made to have a time of oscillation of 1 second. Find the effect on the time, if there is an error of 2mm in the length.
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  2. #2
    Junior Member
    Joined
    Aug 2010
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    This is my solution, somehow answer is different when I calculate without using calculus.

    {\delta L} = 2mm = 0.002m

    \dfrac{dT}{dL}\approx\dfrac{\delta T}{\delta L}

    {\delta T} = \dfrac{\delta T}{\delta L} * {\delta L}

    {\delta T} = \dfrac{-2}{L^2} * 0.002

    {\delta T} = \dfrac{-0.004}{L^2}

    Given that oscillation time, T = 1 second, so L = 2m

    {\delta T} = \dfrac{-0.004}{2^2}

    {\delta T} = -0.001s

    But, the answer given is 0.004s longer.

    Can someone check if my working is right?
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