- #1

Lucy Yeats

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## Homework Statement

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.

## Homework Equations

## 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)

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