Solution (source code)

= Solution

Interpret the supplied real quantity as the <storage modulus> $E'$, with $k$ the <spring> modulus in this continuum representation and $\eta$ the corresponding <viscosity>. Let $\tau=t_R=\eta/k$. Then
$$
E'=\frac{k\omega^2\tau^2}{1+\omega^2\tau^2}.
$$
\b[At high frequency, $\omega\tau\gg1$, the response approaches the <spring> stiffness; at low frequency it becomes much softer]:
$$
\boxed{E'\simeq k\quad(\omega\tau\gg1),\qquad
E'\simeq k\omega^2\tau^2=\frac{\eta^2\omega^2}{k}
\quad(\omega\tau\ll1).}
$$
In the series <Maxwell model>, the <spring> and <dashpot> carry the same <stress> while their strains add. A rapidly changing load allows little viscous flow, so the <spring> dominates the <strain> response. Over a long cycle the <dashpot> has time to deform, giving a small <storage modulus> and a fluid-like low-frequency response. This is generic viscoelastic mechanics, independent of the biological parts deferred above.