A spring has a period of 1 s when a 0.200 kg mass hung from the end of it. If the mass at the end is changed to 0.100 kg, will the period ch

Question

A spring has a period of 1 s when a 0.200 kg mass hung from the end of it. If the mass at the end is changed to 0.100 kg, will the period change?

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Lệ Thu 4 years 2021-08-15T16:21:00+00:00 1 Answers 18 views 0

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  1. phucdien
    0
    2021-08-15T16:22:01+00:00
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    When the mass of the spring changed from 0.2kg to 0.1kg, the time period changed from 1 sec to 0.5 seconds

    Explanation:

    Given-

    Mass, m1 = 0.2kg

    Time period, T1 = 1s

    m2 = 0.1 kg

    T2 = ?

    We know,

    T = 2\pi \sqrt{\frac{m}{k} }

    where,

    T = Time period

    m = mass

    k = spring constant

    From the equation, we can see that T is directly proportion to the square root of mass, m

    T ∝ √m

    So,

    If m1 = 0.2kg , T1 = 1s and m2 = 0.1kg

    The T2 would be:

    \frac{T1}{T2} = \frac{m1}{m2} \\\\\frac{1}{T2} = \frac{0.2}{0.1} \\

    T2 = \frac{1}{2} \\\\T2 = 0.5sec

    Therefore, when the mass of the spring changed from 0.2kg to 0.1kg, the time period changed from 1 sec to 0.5 seconds

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