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Math Help - Need help Mathematical Models!

  1. #1
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    Need help Mathematical Models!

    The period (the time for one complete oscillation) of a pendulum is directly proportional to the square root of the length of the pendulum, and a pendulum of length 8 ft has a period of 2 seconds. Find a mathematical model expressing the period of a pendulum as a function of its length:

    Why is the answer equal to P(x) = \sqrt {\frac{x}{2}}?
    and thanks
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    The period (the time for one complete oscillation) of a pendulum is directly proportional to the square root of the length of the pendulum, and a pendulum of length 8 ft has a period of 2 seconds. Find a mathematical model expressing the period of a pendulum as a function of its length:

    Why is the answer equal to P(x) = \sqrt {\frac{x}{2}}?
    and thanks
    I presume x is the length of the pendulum.

    We know that P(x) is proportional to \sqrt{x}, so let
    P(x) = k \sqrt{x} where k is a constant.

    Since a pendulum of 8 ft has a period of 2 seconds:
    2 = k \sqrt{8}

    k = \frac{2}{\sqrt{8}} = \frac{2}{2\sqrt{2}} = \frac{1}{\sqrt{2}}

    Thus
    P(x) = \frac{1}{\sqrt{2}} \sqrt{x} = \sqrt{\frac{x}{2}}

    -Dan
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