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Accelerating Elastic Pendulum (Lagrangian)

  1. Feb 24, 2008 #1
    1. The problem statement, all variables and given/known data

    A pendulum of mass [tex] m [/tex] is suspended by a massless spring with equilibrium length [tex] L [/tex] and spring constant [tex] k [/tex]. The point of support moves vertically with constant acceleration. Write the Lagrangian of the system and the equation of motion.

    2. Relevant equations

    [tex] L = T - U [/tex]

    [tex] \frac{\partial L}{\partial x_i} - \frac{d}{dt}\frac{\partial L}{\partial \dot{x_i}} = 0 [/tex]

    3. The attempt at a solution

    We can draw a vertical and call the angle of the pendulum to this [tex] \theta [/tex]. I know for an elastic pendulum we have (where [tex] l [/tex] is the variable length) [tex] T = \frac{m}{2} \left( \dot{l^2} + l^2 \dot{\theta^2}\right) [/tex] and [tex] U = \frac{1}{2}k\left(l-L\right)^2 + mgy [/tex] but I'm not sure how to involve the acceleration term. A hint in the right direction would be greatly appreciated :D
  2. jcsd
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