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Scaling factor of a mass spring system

  1. Jan 14, 2013 #1
    1. The problem statement, all variables and given/known data

    A mass spring system carries a mass of 0.4kg. When the point of suspension is made to vibrate verticaly at a frequency of 15Hz resonance occurs. What mass should be added to the 0.4kg in order to reduce the resonant frequency to 10Hz.

    a) 0.20kg
    b) 0.40kg
    c) 0.50kg
    d) 0.60kg

    2. Relevant equations

    T=2∏√(m/k)
    15=2∏√(0.4/k)

    3. The attempt at a solution

    15=2∏√(0.4/k)
    10=2∏√(0.4+x/k)

    Do I rearrange these so I have all the constants on the rhs then equate the lhs and solve for x if that makes sense?
    Any help appreciated
     
  2. jcsd
  3. Jan 14, 2013 #2
    It wouldn't really make sense to try to 'put all the constants on the RHS of the equation' - everything in the first equation is a constant and we know that 'x', the only variable in the second equation, cannot be zero.

    Consider, instead, that 'k', as a property of the spring, will not change between the two scenarios.

    EDIT: Oh, and 'T' represents the period of oscillation rather than the frequency.
     
  4. Jan 14, 2013 #3
    I just realised the T=1/f mistake
    Thanks for the help
     
  5. Jan 14, 2013 #4
    0.06=2∏√(0.4/k)
    0.1=2∏√(0.4+x/k)

    So I still cant seem to get 0.5 out of the rearrangement and equation of the two formula.
     
  6. Jan 14, 2013 #5
    I'm able to get x=0.5kg by that method, actually. If you leave '1/15' on the LHS of the first equation rather than approximating it as '0.06', you should find the same.
     
  7. Jan 19, 2013 #6
    Thanks for the help,
    I love the techniques of physics.
    I got lost in the algebra

    shm_zpsfa23b8c6.jpg
     
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