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Combination of 3 springs at given angles

  1. Jan 26, 2010 #1
    Three springs of spring constant kare connected to a body of mass m and rigid supports, so that the angles are
    A 90 degrees between two and 135 degrees between each of these two and the third.
    B 120 degrees between any 2 adjacent ones.
    Find time period of vibration.
    I worked out a method to solve this question. I added 2 of the spring constants vectorially, first dividing each by the cos of half of the angle between them (45 and 60 degrees) and the third simply as k to get a net spring constant. This gave a correct answer but I don't remember what logic I used and it may not have been correct. Could someone show me the correct solution?
    Last edited: Jan 26, 2010
  2. jcsd
  3. Feb 4, 2010 #2


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    Welcome to PF!

    Hi watermlon! Welcome to PF! :smile:

    What matters is the components of force in each direction.

    If the extension vectors are x y and z (these are not coordinate directions), then the forces are k1x + k2y + k3z

    in this case, k1 = k2 = k3 = k,

    so the total force is k(x + y + z), and you correctly took components along an axis of symmetry (the total of components along the perpendicular axis would be zero). :wink:
  4. Feb 6, 2010 #3
    Thanks, tim. I understand it now.
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