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

Use the E-L 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)^2-mgl(1-cosθ)

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)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Quick Lagrangian of a pendulum question

**Physics Forums | Science Articles, Homework Help, Discussion**