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13 February, 10:28

Here on Earth you hang a mass from a vertical spring and start it oscillating with amplitude 1.9 cm. You observe that it takes 3.0 s to make one round trip. You construct another vertical oscillator with a mass 6 times as heavy and a spring 10 times as stiff. You take it to a planet where gplanet = 8.8 N/kg. You start it oscillating with amplitude 4.8 cm. How long does it take for the mass to make one round trip?

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  1. 13 February, 14:18
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    T = 3.23 s

    Explanation:

    In the simple harmonic movement of a spring with a mass the angular velocity is given by

    w = √ K / m

    With the initial data let's look for the ratio k / m

    The angular velocity is related to the frequency and period

    w = 2π f = 2π / T

    2π / T = √ k / m

    k₀ / m₀ = (2π / T) ²

    k₀ / m₀ = (2π / 3.0) ²

    k₀ / m₀ = 4.3865

    The period on the new planet is

    2π / T = √ k / m

    T = 2π √ m / k

    In this case the amounts are

    m = 6 m₀

    k = 10 k₀

    We replace

    T = 2π√6m₀ / 10k₀

    T = 2π √6/10 √m₀ / k₀

    T = 2π √ 0.6 √1 / 4.3865

    T = 3.23 s
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