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6 January, 08:20

Suppose that the period of a particular ideal mass-spring system is 5 s. What would be the period of the system if the mass were two times the original mass?

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  1. 6 January, 10:19
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    Answer: T2 = 7.07s

    Explanation: The period of a loaded spring of spring constant k and mass m is given by

    T = 2π √m/k

    With 2π constant and k, it can be seen with little algebra that

    T² is proportional to mass m

    Hence (T1) ²/m1 = (T2) ²/m2

    Where T1 = 5, T2 = ?, let m1 = m hence m2 = 2m.

    By substituting, we have that

    5²/m = (T2) ²/2m

    25 / m = (T2) ²/2m

    25 * 2m = (T2) ² * m

    25 * 2 = (T2) ²

    50 = (T2) ²

    T2 = √50

    T2 = 7.07s
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