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"the period of a pendulum, T (in seconds) varies directly with the square root of the length of the pendulum, L (in centimeters)". Given that a pendulum of length 9cm has a period of 0.63 seconds, find:

a) The period of a pendulum of length 25cm

b) The length of a pendulum whose period is 1.5 seconds,

thanks :)

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2 answers
  1. Given
    T seconds =k √L (cm)

    where k is an arbitrary constant to be determined.

    Also given

    0.63=k√9
    Therefore we can determine the constant k.
    k=0.63/√9=0.21

    The relation now reads:
    T(L)=0.21√L
    where T is period in seconds
    and L is length of pendulum in cm.

    The problem reduces to:
    a) T(25)=?
    b) if T(L)=1.5 s, what is L?

    Can you take it from here?

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  2. T = k√L
    so, T/√L is constant.

    (a) .63/√9 = T/√25

    (b) .63/√9 = 1.5/√L

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