Secular phase integral for proportional mass growth
= Secular phase integral for proportional mass growth
{title2=$\Phi(t)=\int_0^t g(t\prime)\,dt\prime$}
If both precession and forcing in $\dot z=ig(t)(z-z_f)$ share a common mass factor while $z_f$ stays fixed, then $z=z_f+(z(0)-z_f)\exp(i\int_0^t g(t\prime)\,dt\prime)$. The <Argand diagram> circle is unchanged; only its traversal speed varies. With $g(t)=g_f t/t_p$, the phase is $g_ft^2/(2t_p)$.