= Solution
A <polymer> melt has an observation-time-dependent response because chains need time to rearrange. Short compared with their terminal relaxation time, entangled chains constrain one another and can store elastic <free energy>. Long compared with that time, chains escape their original constraints by <reptation> and the uncrosslinked melt flows. A permanently crosslinked <elastomer> instead retains a long-time elastic modulus.
A single-time approximation is the <Maxwell fluid>: a spring of shear modulus $G$ and a viscous dashpot of <viscosity> $\eta$ in series. Their common <stress> and additive shear strains give $\dot\gamma=\dot\sigma/G+\sigma/\eta$, with relaxation time $\tau=\eta/G$. For sinusoidal deformation proportional to $e^{i\omega t}$, the <storage modulus> and <loss modulus> are
$$
G'=G\frac{(\omega\tau)^2}{1+(\omega\tau)^2},\qquad G''=G\frac{\omega\tau}{1+(\omega\tau)^2}.
$$
At low frequency $G''\simeq\eta\omega$ dominates; at high frequency within this coarse-grained model $G'\simeq G$ dominates. Real melts have a spectrum of relaxation times and additional segmental or glassy regimes, so the single-time model does not describe every frequency. A step-strain experiment measures the decay of <stress>, whereas oscillatory rheometry separates stored energy from dissipated energy through the phase of the response.
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