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25 July, 07:10

When a force of 20.0 N is applied to a spring, it elongates 0.20 m. Determine the period of oscillation of a 4.0-kg object suspended from this spring.

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  1. 25 July, 07:29
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    1.26 secs.

    Explanation:

    The following data were obtained from the question:

    Force (F) = 20 N

    Extention (e) = 0.2 m

    Mass (m) = 4 Kg

    Period (T) =.?

    Next, we shall determine the spring constant, K for spring.

    The spring constant, K can be obtained as follow:

    Force (F) = 20 N

    Extention (e) = 0.2 m

    Spring constant (K) = ... ?

    F = Ke

    20 = K x 0.2

    Divide both side by 0.2

    K = 20/0.2

    K = 100 N/m

    Finally, we shall determine the period of oscillation of the 4 kg object suspended on the spring. This can be achieved as follow:

    Mass (m) = 4 Kg

    Spring constant (K) = 100 N/m

    Period (T) = ... ?

    T = 2π√ (m/K)

    T = 2π√ (4/100)

    T = 2π x √ (0.04)

    T = 2π x 0.2

    T = 1.26 secs.

    Therefore, the period of oscillation of the 4 kg object suspended on the spring is 1.26 secs.
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