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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 3

Equating the two linearized expressions for $p(a,t)-p_\infty$ from parts (iii) and (iv) gives
$$
\rho a_0^2\log\frac{b_0}{a_0}\,\ddot\epsilon+2p_\infty\epsilon=0.
$$
This is the equation of <simple harmonic motion>. Thus the bubble performs with <angular frequency>
$$
\boxed{\omega=\left(\frac{2p_\infty}
{\rho a_0^2\log(b_0/a_0)}\right)^{1/2}}.
$$
This is the .

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 3 / 16C / b / v / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 3 / 16C / b / v / Solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 3 / 16C / b / v / Solution

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