Pre-Calculus

The Period T, in seconds, of a pendulum depends on the distance, L, in meters, between the pivot and the pendulum's centre of mass. If the initial swing angle is relatively small, the period is given by the radical function T=2pi(sqrtL/g) where g represents acceleration due to gravity (approximately 9.8m/s^2 on Earth.) Jeremy is building a machine and needs it to have a pendulum that takes 1 second to swing from one side to the other how long should the pendulum be, in centimeters?

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  1. in MKS units,
    1 = 2π√(L/9.8)
    (1/2π)^2 = L/9.8
    L = 9.8/(2π)^2 = ...
    convert to cm

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  2. The full period is 2 seconds.

    Divide 2 / 2 x Pi. Square this equation so you have 4 / 4 Pi squared. Then times that answer by 980 (9.8 m to Cm)

    You should get the correct answer of approximately 99 Cm for L

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