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## Homework Statement

A simple pendulum with mass m and length ℓ is suspended from a point which moves

horizontally with constant acceleration a

> Show that the lagrangian for the system can be written, in terms of the angle θ,

L(θ, θ, t˙ ) = m/2(ℓ^2θ˙^2 + a^2t^2 − 2aℓtθ˙ cosθ) + mgℓ cos θ

> Determine the Euler–Lagrange equation for the system.

## Homework Equations

## The Attempt at a Solution

I thought I could prove that l^2θdot^2 + a^2t^2 - 2altθdotCosθ was v^2 using relative velocities: v^2 = (at - lθdot)^2 = (l^2θ^2 + a^2t^2 - 2altθdot). But I've no idea where the Cosθ is coming from, so I can only assume I'm wrong somewhere.

I also can't understand how V = -mglCosθ

h for this pendulum should be l(1 - Cosθ) shouldn't it?

Any help's appreciated. Thanks.