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Thread: I need help with this question.

  1. #1
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    I need help with this question.

    the question is:

    The time, T, in seconds, that a pendulum takes to do a complete oscillation is given by the
    formula
    T = 2PI
    where l is the length of the pendulum, in metres, and g is the acceleration due to gravity.
    Take the value of g to be 9.807 m/s2.
    In St. Isaac’s cathedral in St. Petersburg there is a pendulum of length 94 m.
    18 (a) (i) Calculate the value of T for this pendulum.
    Give all the figures in your calculator display.
    Give your answer as a decimal.

    Can somebody explain to me how to do this,i already know the answer but i want to know how to do it.(This is a past GCSE)Thanks.
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  2. #2
    Super Member Bacterius's Avatar
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    Are you sure you haven't posted your formula wrong ?
    Because the real formula is :

    $\displaystyle T = 2 \pi \sqrt{\frac{L}{g}}$ where $\displaystyle L$ is the length of the pendulum and $\displaystyle g \approx 9.807$.

    Anyway, you are given the length of the pendulum, and you know the constant $\displaystyle g$. Just plug the values into your equation to find $\displaystyle T$ for this pendulum.

    So, you find $\displaystyle T = 2 \pi \sqrt{\frac{94}{9.807}} \approx 19,452512699185704931509913432719$ seconds

    Yes I have a lot of figures because I use a high-precision calculator on your calculator you should have the answer rounded around 10 decimal digits. Thus, you find $\displaystyle T \approx 19,45251269$ seconds.

    I do not get the last question. $\displaystyle \pi$ is irrationnal, so you cannot express $\displaystyle T$ as a fractional number. Do they just mean round it off sensibly ?
    Last edited by Bacterius; Dec 8th 2009 at 03:53 AM.
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  3. #3
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    Quote Originally Posted by Bacterius View Post
    Are you sure you haven't posted your formula wrong ?
    Because the real formula is :

    $\displaystyle T = 2 \pi \sqrt{\frac{L}{g}}$ where $\displaystyle L$ is the length of the pendulum and $\displaystyle g \approx 9.807$.

    Anyway, you are given the length of the pendulum, and you know the constant $\displaystyle g$. Just plug the values into your equation to find $\displaystyle T$ for this pendulum.

    So, you find $\displaystyle T = 2 \pi \sqrt{\frac{94}{9.807}} \approx 60,224270304362305376871311925823$ seconds

    Yes I have a lot of figures because I use a high-precision calculator on your calculator you should have the answer rounded around 10 decimal digits. Thus, you find $\displaystyle T \approx 60,22427030$ seconds.

    I do not get the last question. $\displaystyle \pi$ is irrationnal, so you cannot express $\displaystyle T$ as a fractional number. Do they just mean round it off sensibly ?
    Yeh i just copy and pasted that and never realy read over it lol but yeh it did mean
    $\displaystyle T = 2 \pi \sqrt{\frac{L}{g}}$i couldnt be botherd to get a calculator xD so tryed to do it in my head.

    it sais calc the value of T give all the figs in calcs display and to give your answer as a decimal.

    Let me go get my calculator to make my life a bit easyer
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  4. #4
    Super Member Bacterius's Avatar
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    You should get a calculator, it is useful ...
    Otherwise, I answered the part on the calculator's display (just to it on your calculator and copy on your answer booklet), but I don't know what you mean by giving the answer as a decimal. No additional information ?
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  5. #5
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    I just looked at the answer they give on the site and its 19.4525127 which is what i got when i just did it in my calculator. so 60.(loads of numbers) is rong?
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  6. #6
    Super Member Bacterius's Avatar
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    Oh yeah I forgot to do the square root in my calculations, my mistake , that answer is correct
    I'll edit my previous posts, thanks for noticing.
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  7. #7
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    Could you tell me how i calculate the length of a pendulum that will give a value of T=1?
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  8. #8
    Super Member Bacterius's Avatar
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    You need to solve this equation for $\displaystyle L$ :

    $\displaystyle 1 = 2 \pi \sqrt{\frac{L}{g}}$

    Extract annoying numbers :

    $\displaystyle \frac{1}{2 \pi} = \sqrt{\frac{L}{g}}$

    Take the square of both sides to get rid of the square root :

    $\displaystyle (\frac{1}{2 \pi})^2 = \sqrt{\frac{L}{g}}^2$

    $\displaystyle \frac{1}{4 \pi^2} = \frac{L}{g}$

    Multiply by $\displaystyle g$ on both sides :

    $\displaystyle \frac{1}{4 \pi^2} \times g = \frac{L}{g} \times g$

    $\displaystyle \frac{g}{4 \pi^2} = L$

    So the length of a pendulum with a period of $\displaystyle 1$ second would be $\displaystyle L = \frac{g}{4 \pi^2} \approx 0.248414$ metres, so about $\displaystyle 25$ cm
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  9. #9
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    Smile

    Quote Originally Posted by Ben1191 View Post
    Could you tell me how i calculate the length of a pendulum that will give a value of T=1?
    $\displaystyle T=2\pi \sqrt{\frac{L}{g}}$
    square both sides
    $\displaystyle T^2=4\pi^2\frac{L}{g}.$
    therefore,
    $\displaystyle L=\frac{T^2\times g}{4\pi ^2}$
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  10. #10
    Super Member Bacterius's Avatar
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    A bit late Raoh
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  11. #11
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    Smile

    Quote Originally Posted by Bacterius View Post
    A bit late Raoh
    I'm too slow
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  12. #12
    Super Member Bacterius's Avatar
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    Yet you made me realize that I didn't have to isolate the square root to remove it since there are only multiplications !
    Looking for an excuse ...
    Let's say I did it for the example
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