= Solution
Here the <complex viscoelastic modulus> is a stress-to-strain response coefficient, rather than a complex number's absolute value. Use strain $\gamma(t)=\operatorname{Re}(\gamma_0e^{i\omega t})$ and stress $\tau(t)=\operatorname{Re}[G^*(\omega)\gamma_0e^{i\omega t}]$, with
$$
\boxed{G^*=G'+iG'',\qquad\tau=\gamma_0(G'\cos\omega t-G''\sin\omega t).}
$$
The <storage modulus> $G'$ measures the elastic component; the <loss modulus> $G''$ measures dissipation. The mean power per volume is $\omega\gamma_0^2G''/2$, and the energy dissipated per cycle is $\pi\gamma_0^2G''$, fixing the sign convention.
A Hookean solid has $G^*=G_0$, while a Newtonian fluid has $G^*=i\omega\eta$. The <Maxwell model> interpolates with $G^*=G_0i\omega\tau_R/(1+i\omega\tau_R)$, giving $G'=G_0(\omega\tau_R)^2/[1+(\omega\tau_R)^2]$ and $G''=G_0\omega\tau_R/[1+(\omega\tau_R)^2]$. It is fluid-like at low frequency and elastic on times short compared with relaxation time $\tau_R$.
A <rheometer> imposes <small-amplitude oscillatory shear> and resolves the torque amplitude and phase relative to the imposed motion. The <torsional measurement of a complex shear modulus> makes the conversion from torque and twist to $G^*$ explicit. A frequency sweep locates relaxation scales; keeping the strain small tests the linear-response assumption.
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