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Spring Velocity question

  1. Sep 29, 2013 #1
    1. The problem statement, all variables and given/known data
    A mass of 0.3kg is suspended from a spring of stiffness 200Nm. If the mass is displaced by 10mm from its equilibrium position and released for the resulting vibration, calculate:
    The mass required to produce double the maximum velocity calculated in question 2 using the same spring and deflection. The velocity in question 2 being 0.26ms-1.


    2. Relevant equations
    V=Aωcos(ωt+∅)
    ω=√k/m

    3. The attempt at a solution
    So A=0.01 v= 0.52MS-1.
    So transposing ωcos = 0.52/0.01 = 52rads.

    Now with these numbers i can find the mass.
    ω=√k/m
    Transposing m = k/m^2
    Mass = 0.07kg.

    Now the laws of physics are telling me this answer cannot be right. If an object with a mass of 0.3kg possesses a velocity of 0.26ms-1, then an object with a velocity of 0.52ms-1 should be greater than 0.07kg. The velocity is higher so surely the mass must be greater. Where am i going wrong with this!. Any help would be appreciated.
     
  2. jcsd
  3. Sep 30, 2013 #2

    haruspex

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    I see no reason why a greater mass should mean a higher velocity. Think about the acceleration. A higher mass has greater inertia, but the same deflection of the same spring only produces the same force.
    Maybe you are subconsciously taking the greater mass case also to have a greater displacement as part of a general scaling up. In that case you could get a greater velocity.
     
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