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27 September, 05:16

A mass oscillates on the end of a spring, both on earth and on the moon. where is the period the greatest?

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  1. 27 September, 05:36
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    Draw a diagram to illustrate the problem as shown below.

    m = mass of the object

    x = displacement

    k = spring constant

    g = acceleration due to gravity.

    The driving force of mg (weight) is opposed by the spring restoring force

    of - kx.

    The equation of motion is

    mg - kx = m x''

    or

    x'' + (k/m) = g

    For oscillatory motion, the homogeneous solution of the ODE yields

    ω² = 2π/T = k/m

    where

    T = period of oscillation

    ω = circular frequency

    The period is T = 2π√ (m/k)

    Answer:

    Th period is independent of g, therefore the period will be the same on earth and the moon.
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