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A 0.5 Kg mass is supported by a spring . The system is set in vibration at its natural frequency of 4 Hz with an amplitude of 5 Cm.Find the spring constant .

  • physics -

    Use the formula for natural frequency f:

    f = [1/(2 pi)]*sqrt(k/m)

    Rearrange it to solve for the spring constant k, knowing frequency (f) and mass (m).

    4 pi^2 * f^2 * m = k

    The amplitude does not matter in this case. The units of the answer (k) will be Newtons per meter if f is in Hz and m is in kg, since

    kg * s^-2 = (kg*m/s^2)/m = N/m

  • physics -

    I had already used the above formula and calculated k = 315.8 N/m
    But the book answer is k = 101 N/m
    Hence this query

  • physics -

    The book answer appears to be wrong by a factor of pi

  • physics -

    Thanks a lot

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