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29 March, 17:46

A science museum has asked you to design a simple pendulum that will make 29.0 complete swings in 83.0 s. What length should you specify for this pendulum?

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  1. 29 March, 20:33
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    2.035 m

    Explanation:

    The period of oscillation in a simple pendulum when the angle of swing is not too large relates to the length with the formula:

    T = 2π√ (L/g) where L is the length of the pendulum in meters, T is the period in seconds, and g is acceleration due to gravity in m/s^2

    T can be calculated by

    T = time of oscillations / number of complete oscillations (complete swings)

    T = 83/29 = 2.862s

    Deriving an equation for L

    T = 2π √ (L/g)

    Divide both side by 2π

    T / 2π = √ (L/g)

    Square both sides

    T^2/4π^2 = L/g

    Cross multiply

    T^2 * g / 4π^2

    Substitute in the values of the terms

    (2.862^2) * 9.81 / (4 * 3.142 * 3.142) = 2.035m
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