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Homework Help: Three Springs in an Equilateral Triangle

  1. Jan 4, 2015 #1
    1. The problem statement, all variables and given/known data

    Three identical point masses of mass m each are placed at the vertices of an equilateral triangle and joined through springs of equal length and spring constant k . The system is placed on a smooth table. If the masses are displaced a little towards the centroid of the triangle then time period of oscillation of the system is :

    2. Relevant equations
    F = -k x
    ω = √(k/m)

    3. The attempt at a solution

    Consider one mass which is displaced from the mean position by x units. The two forces acting on it are k*x* cos(30 Degree) each inclined at an angle of 60 Degrees.

    That would mean that the force acting on it is actually (3/2)*k*x, or the equivalent spring constant is (3/2)*k.

    But that gives an weird time period which isn't in the options!
  2. jcsd
  3. Jan 4, 2015 #2


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    Science Advisor
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    Gold Member

    "Masses," plural.
    It's necessary to solve the stated problem rather than an intuitive simplification of the statement.
  4. Jan 4, 2015 #3
    In what direction does the mass move?
    If S is the side of the triangle, what is the radius of the circumscribed circle?
    If S changes by ΔS, by how much does the radius of the circumscribed circle change?
    What is the tension in each spring if S changes by ΔS.
    What is the resultant F of the adjacent tension forces on the mass if S changes by ΔS?
    How is the resultant force F on the mass related to its displacement?

  5. Jan 4, 2015 #4
    1. The mass moves towards along the radius of the circumcircle.

    2. The radius(R) of the circumcircle is S/√3

    3. ΔR = ΔS/√3

    4. T = k ΔS/√3

    5. F = k ΔS

    Could you please tell if these are correct?
  6. Jan 4, 2015 #5

    T = kΔS

    Now, combine these to express F in terms of ΔR.

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