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Plotting the graph of pendulum period versus length

  1. Apr 8, 2014 #1
    why do we square the value of T ( time period) while plotting the graph of effect on time period of a pendulum with change in its effective length ?

    also while deriving the formula of
    T=2∏√(l/g)

    why do we take T^2 = 1/g.

    Whats the need for squaring the time period ?
     
  2. jcsd
  3. Apr 8, 2014 #2
    Because for the convenience. even if you dont square Timeperiod nothing will change, you will always get a parabola with T>0 and l>0
     
  4. Apr 8, 2014 #3

    jtbell

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    Staff: Mentor

    To get a straight-line graph, you can plot either T2 versus l, or T versus √l. If your calculator doesn't have a square-root key, the first method is easier.
     
  5. Apr 8, 2014 #4
    More generally if you are trying to identify the relationship between two quantities it is difficult to look at a curve and say it is an arc of a circle, parabola, hyperbola, exponential or whatever. However it is much easier to recognise a straight line. So we transform the equation to produce a linear relationship. In this case squaring the equation gives a straight line by plotting t2 against l.
    This gives a straight line whose gradient would be is 4∏2/g.
     
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