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Math Help - Algebra II

  1. #1
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    Algebra II

    1.) The period for the pendulum in a clock is givin by: T(L)=2(3.14)√L/32, where T(L) is the period in seconds and L is the length in ft.
    a) Find the period of a pendulum that is 18 inches long

    b) find the period of a Foucault pendulum that is 72 ft. long

    c) How long is the pendulum that has a period of 7.5 seconds?


    Thank you :]
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by ep78 View Post
    1.) The period for the pendulum in a clock is givin by: T(L)=2(3.14)√L/32, where T(L) is the period in seconds and L is the length in ft.
    a) Find the period of a pendulum that is 18 inches long

    b) find the period of a Foucault pendulum that is 72 ft. long

    c) How long is the pendulum that has a period of 7.5 seconds?


    Thank you :]
    For the first two, substitute the lengths into the equation.

    a) Note that we need to convert the length from inches to feet: 18\text{ in}=1.5\text{ ft}

    Thus, T(1.5)=2\pi\sqrt{\frac{1.5}{32}}

    Just plug this into a calculator, where \pi\approx 3.14

    b) T(72)=2\pi\sqrt{\frac{72}{32}}

    Just plug this into a calculator, where \pi\approx 3.14

    c) Here, we know that T=7.5\text{ sec}, but we want to find L:

    T=2\pi\sqrt{\frac{L}{32}}\implies \frac{T}{2\pi}=\sqrt{\frac{L}{32}}\implies \bigg(\frac{T}{2\pi}\bigg)^2=\frac{L}{32}\implies L=32\bigg(\frac{T}{2\pi}\bigg)^2

    Now plug in T=7.5 and plug this into your calculator:

    L=32\bigg(\frac{7.5}{2\pi}\bigg)^2\approx ......, where \pi\approx 3.14

    Does this make sense?

    --Chris
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  3. #3
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    very much so..thanks so much!
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