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20 July, 12:12

A vertical scale on a spring balance reads from 0 to 200 / rm{N}. The scale has a length of 10.0 / rm{cm} from the 0 to 200 / rm{N} reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.05 / rm{Hz}.

Ignoring the mass of the spring, what is the mass m of the fish?

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  1. 20 July, 12:16
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    m = 12.05 kg

    Explanation:

    Spring constant in K, N/m

    K = 200/10 * 100

    K = 2000 N/m

    Angular Frequency = sqrt (Spring constant / (Mass)

    ω = 2 π f

    ω = 2π * 2.05 Hz = 12.8805 rad/s

    ω^2 = Spring constant / Mass

    Mass = Spring constant / ω^2

    ω^2 = 165.907 rad^2/s^2

    m = 2000 (N/m) / 165.907 (rad^2/s^2)

    m = 12.05 kg
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