Solution
= Solution
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 <small oscillations> with <angular frequency>
$$
\boxed{\omega=\left(\frac{2p_\infty}
{\rho a_0^2\log(b_0/a_0)}\right)^{1/2}}.
$$
This is the <small oscillation of a planar gas bubble in an annular liquid>.