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Math Help - Simple Harmonic Motion

  1. #1
    Senior Member tukeywilliams's Avatar
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    Simple Harmonic Motion

    A block is hung on a spring, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried into space. The 2 blocks are attached to the ends of a spring, and the system is taken out into space on a space walk. The spring is extended, and the system is released to oscillate while floating in space. What is the frequency of oscillation for this system, in terms if f
    I know the answer is sqrt(2)f . But how do we get this?

    Thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tukeywilliams View Post
    A block is hung on a spring, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried into space. The 2 blocks are attached to the ends of a spring, and the system is taken out into space on a space walk. The spring is extended, and the system is released to oscillate while floating in space. What is the frequency of oscillation for this system, in terms if f
    I know the answer is sqrt(2)f . But how do we get this?

    Thanks
    The frequency of oscillation of a spring can be found using the formula:
    f = sqrt{k/M}
    where k is the spring constant and M is the reduced mass attached to the spring. (1/M = 1/m1 + 1/m2 where m1 and m2 are the masses attached to each end of the spring.)

    On Earth, fE is measured and we have M = m, the mass of the block: fE = sqrt{k/m}
    In space, fS is measured and we have M = m/2: fS = sqrt{2k/m}

    fS = sqrt{2}*sqrt{k/m} = sqrt{2}*fE

    -Dan
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