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?

Answers

  1. 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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