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The length of time that it takes for a pendulum to make one complete swing depends on the length of the pendulum. The time in seconds, T, is related to the length in meters, L, through the equation:
T=2π√((L)/(9.8)) [it is all under square root]

Q1: write in function notation
Q2: state the domain of this function
Q3: Graph the function pendulums up to 20 m in length
Q4: when T = 10, how long would the pendulum be
Q5: If the pendulum was twice as heavy, what would T be?

  • math -

    T(L) = 2π √(L/9.8)

    domain: any positive value of L

    graph: you'll have to do this, by making a table of values, pick any L, use your calculator to find T
    plot all your (L,T) s

    when T = 10
    10 = 2π √(L/9.8)
    square both sides
    100 = 4π^2 (L/9.8)
    980/(4π^2) = L = 24.824 m

    The weight of the pendulum is not a factor, T would be the same.

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