1. Limited time only! Sign up for a free 30min personal 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!

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

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Accelerating Elastic Pendulum (Lagrangian)
  1. Lagrangian of pendulum (Replies: 2)