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Homework Help: Differential equation of spring-mass system attached to one end of seesaw

  1. Aug 31, 2009 #1
    please help me to find differential equation of spring-mass system attached to one end of seesaw.

    case 1: Seesaw is balanced with its fulcrum point or pivotal point. At one end of seesaw, the spring (with spring constant K1) is attached. Now the seesaw has total mass M which is attached to spring, form a spring-mass system. I confuse on this point that the oscillation of seesaw will be around pivotal point. Then what is differential equation of spring-mass system.

    case 2: The same case with both ends of Seesaw is attached with springs having spring constant K1 and K2. Then what is differential equation of this system.
  2. jcsd
  3. Sep 1, 2009 #2
    [tex]\frac{L^2}{4} \theta K+J\ddot{\theta} = 0[/tex]
    [tex]J = \frac{1}{12}ML^2[/tex]
    case 1: K = K1
    case 2: K = K1+K2

    Assuming uniform seesaw, pivot is center of mass (also geometry center). If otherwise seesaw is not uniform, J will change accordingly. If pivot is not geometry center, the equation will be slightly different.
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