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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2026

Paper 2

With $x=\ell\sin\theta$ and $y=-at^2/2-\ell\cos\theta$, discard a total <derivative> from the <kinetic energy> to obtain
$$
L=\tfrac12m\ell^2\dot\theta^2+ m\ell(g-a)\cos\theta.
$$
\b[Thus $\ddot\theta+(g-a)\sin\theta/\ell=0$. If $a=g$, then $\ddot\theta=0$: the pendulum is weightless in the lift and rotates uniformly (or remains fixed).]

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 8A / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 8A / a / Solution

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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 8A / a / Solution

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