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Angular frequency of plank attached to spring

  1. Feb 25, 2016 #1
    1. The problem statement, all variables and given/known data
    A horizontal plank (mass 2kg, length 1m) is pivoted at one end. A spring (k=1000N/m) is attached at the other end. Find the angular frequency for small oscillations.

    Answer: ω=39rad/s

    2. Relevant equations
    ω = √(mgd + kΔxd/I)
    I think I would be treating the plank as a long thin rod with rotational axis through the end (since I'm not provided with the dimensions of the plank), so I = 1/3mL2 + md2
    Where L: length of the rod, d: distance between pivot and rod's centre of mass (d=L/2)

    3. The attempt at a solution
    I = 1/3mL2 + md2 = 1/3mL2 + m(L/2)2

    ω = √(mgd + kΔxd/I)
    mgd component --> mg(L/2)
    kΔxd component --> mg(L/2)2

    Substituting all the known values...
    ω = √[(2)(9.8)(1/2) + 1000(12)] / [(1/3)(2)(12) + 2(1/2)2]
    ω = √1009.8/1.16 = 29.4

    Still not getting the correct answer.
     

    Attached Files:

  2. jcsd
  3. Feb 25, 2016 #2

    haruspex

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    Not so.
     
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