Pressure in radially symmetric annular potential flow

If the pressure at $r=b(t)$ is $p_{\infty }$, the Unsteady Bernoulli equation gives

For $a=a_0(1+ϵ)$, equilibrium outer radius $b_0$, and a bubble gas obeying $p_0\pi a^2=\text{constant}$, the linearization isThe bubble therefore undergoes simple harmonic motion with