(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using the usual angle [tex]\phi[/tex], as generalized coordinate, write down the Lagrangian for a simple pendulum of length l suspended from the ceiling of an elevator that is accelerating upward with constant acceleration a. Find the Lagrangian equation of motion and sho that it is the same as that for a normal, nonaccelerating pendulum except that g has been replaced by g+a.

2. Relevant equations

Lagrangian is L=Kinetic energy- potential energy=T-U

3. The attempt at a solution

I need to find the kinetic energy and potential energy, which i know that T=1/2mv^{2}and U=mgh.

So I think that T=1/2ml^{2}[tex]\phi[/tex] '^{2}(the phi has a prime, its hard to see) and

U=mgl(1-cos[tex]\phi[/tex])

However, I don't think that these are right because I didn't do anything with the fact that it is in an elevator accelerating. Any help?

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# Simple Pendulum in an elevator

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