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Homework Help: Frequency problem (static equilibrium)

  1. Jan 12, 2016 #1
    1. The problem statement, all variables and given/known data
    The lower end of a uniform beam is attached to a vertical wall by a frictionless pivot. The beam extends away from the wall and upward, making a 62° angle with the wall, and it is held in place by a horizontal wire attached from its upper end to the wall. The wire's length and mass are 4.98-m, 0.737-kg and the beam's weight is 349-N. The speed of sound is 344 m/s. When the wind blows, the wire vibrates in its 4th overtone

    2. Relevant equations
    flambda = v

    3. The attempt at a solution
    First I wanted to find the tension force so I can find v...

    [itex] v = \sqrt {\frac{F_{t}}{\mu}} [/itex]
    Because the system is in static equilibrium I set [itex] \tau_{F_{g}} = \tau_{T} [/itex] .... [itex] \frac{m_{b}gL}{2} * sin(\theta) = TLcos(\theta) [/itex] .... [itex]T = \frac{m_{b}g}{2}tan(\theta) [/itex]

    Thus, [itex] v= \sqrt{\frac{\frac{m_{b}g}{2}tan(\theta)}{\frac{0.737}{4.98}}} = 9.456[/itex]
    [itex] \lambda_{5} = \frac{2L}{5} [/itex] ... solving for [itex] f* \frac{2L}{5} = 9.456 [/itex], I get the frequency is 4.747.... which isnt the correct answer.... can someone tell me where I'm going wrong? Thanks.
  2. jcsd
  3. Jan 12, 2016 #2


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    Homework Helper

    Check the value of v.
  4. Jan 12, 2016 #3
    bloody hell.
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