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Math Help - Variation - Please Help

  1. #1
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    Exclamation Variation - PLEASE Help!?!

    The period T of a simple pendulum is the time taken for one complete small oscillation. T varies directly with the square root of its length L. When the length of the pendulum is 98 cm, the period is exactly 2 seconds.

    i) What length should the pendulum be if its period is to be halved?

    ii) A grandfather clock is regulated by this pendulum. The pendulum is lengthened to 1 m and the clock started at noon. Calculate the actual time, to the nearest second, when the clock first shows 1 o'clock.

    For i) I worked out the length as 1/4 and ii) the time is 2:01. My answers dont look right. Could someone please help?
    Last edited by xwrathbringerx; October 5th 2008 at 06:44 PM.
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    The period T of a simple pendulum is the time taken for one complete small oscillation. T varies directly with the square root of its length L. When the length of the pendulum is 98 cm, the period is exactly 2 seconds.

    i) What length should the pendulum be if its period is to be halved?

    ii) A grandfather clock is regulated by this pendulum. The pendulum is lengthened to 1 m and the clock started at noon. Calculate the actual time, to the nearest second, when the clock first shows 1 o'clock.

    For i) I worked out the length as 1/4 and ii) the time is 2:01. My answers dont look right. Could someone please help?

    As the period varies directly with the square root of its length you have:

    T=k\sqrt{L}

    for some constant k.

    With L in metres, you are told that:

    T=k\sqrt{0.98}=2 ,

    so:

    k=2/\sqrt{98}

    Now what is the period when L=1?

    One hour is 1800 swings of a 2 second pendulum, at what time does the 1 metre pendulum complete 1800 swings?

    RonL
    Last edited by CaptainBlack; October 6th 2008 at 12:05 PM.
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  3. #3
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    Exclamation

    Ummm is it 37 s past 1 o'clock?
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  4. #4
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    Quote Originally Posted by xwrathbringerx View Post
    Ummm is it 37 s past 1 o'clock?
    The period of the 1 m pendulum is:

    \tau=2/\sqrt{0.98} s

    The time for 1800 swings is:

    1800 \times \tau=3600/\sqrt{0.98} s

    which is:

    1800 \times \tau-2\times 1800=3600/\sqrt{0.98}-3600=36.55 s

    longer than 1800 swings of the 2 s pendulum.

    So yes, the time rounded to the nearest second is 37 s past 1 o'clock

    RonL
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