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19 August, 12:16

A 1.9 g spider is dangling at the end of a silk thread. you can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. you soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap at a frequency of 1.2 hz. what is the spring constant of the silk thread?

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  1. 19 August, 12:24
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    M = 1.9 g = 1.9 x 10⁻³ kg, the mass of the spider

    f = 1.2 Hz, the fundamental frequency

    The circular frequency is

    ω = 2πf = 2.4π cycles/s

    For oscillatory motion,

    ω² = k/m

    where k = the spring constant.

    Therefore

    k/m = (2.4π) ²

    k = (1.9 x 10⁻³ kg) * (2.4π 1/s) ² = 0.108 N/m

    Answer: 0.108 N/m
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