1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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 :
    A)2π√(m/k)
    B)2π√(m/2k)
    C)2π/√(m/3k)
    D)2π√(m/5k)

    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

    Bystander

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    "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?

    Chet
     
  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
    F=2Tcos(30)=T√3

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

    Chet
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted