Quick Lagrangian of a pendulum question
1. The problem statement, all variables and given/known data
Use the EL equation to calculate the period of oscillation of a simple pendulum of length l and bob mass m in the small angle approximation. Assume now that the pendulum support is accelerated in the vertical direction at a rate a, ﬁnd the period of oscillation. For what value of a the pendulum does not oscillate? Comment on this result. 2. Relevant equations 3. The attempt at a solution I've got the first bit: L=(m/2)(l^2)(dθ/dt)^2mgl(1cosθ) E.O.M.: d2θ/dt2+(g/l)sinθ=0 d2θ/dt2+(g/l)θ=0 in the small angle approximation, which is S.H.M. with ω^2=√(g/l) (though I'm not sure about this as there's no minus sign in the E.O.M.) so T=2pi√(l/g) For the next bit, I just need help setting up the equations: So the generalized coordinates are θ and a. Are the following correct?: x=lsinθ y=lcosθ+at (taking the origin as the point from which the pendulum is swinging) 
Re: Quick Lagrangian of a pendulum question
Quote:

Re: Quick Lagrangian of a pendulum question
Thanks for pointing that out, I'll correct that in the first post. :)

Re: Quick Lagrangian of a pendulum question
Any help would be great. :D

Re: Quick Lagrangian of a pendulum question
Should y be lcosθ+0.5at^2 instead?

Re: Quick Lagrangian of a pendulum question
Quote:
Quote:
"a" is not a coordinate. Actually only θ is a generalized coordinate since the y coordinate of the support is constrained to be y=0.5at^2. The angle θ is the only freedom that the system has. 
Re: Quick Lagrangian of a pendulum question
Great, I've got it now.
Thanks! :) 
All times are GMT 5. The time now is 06:46 PM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums