= Solution
The <dynamic modulus>, or <complex viscoelastic modulus>, is the ratio of complex <stress> amplitude to complex <strain> amplitude in the periodic steady response:
$$
\sigma(t)=\Re[\widehat\sigma e^{i\omega t}],\qquad
\epsilon(t)=\Re[\widehat\epsilon e^{i\omega t}],\qquad
\boxed{G^*(\omega)=\frac{\widehat\sigma}{\widehat\epsilon}=G'+iG''.}
$$
This defines the sign convention; for passive response the <loss modulus> is nonnegative at positive frequency. A <Newtonian fluid> obeys $\sigma=\eta\dot\epsilon$, while a <Hooke's law> solid obeys $\sigma=G_0\epsilon$. Hence
$$
\boxed{G^*_{\mathrm{Newtonian}}=i\omega\eta,\qquad
G^*_{\mathrm{Hookean}}=G_0.}
$$
The first is purely dissipative and the second purely elastic. Here $\epsilon$ denotes the scalar deformation used in the problem, with any shear-versus-extension geometric factors already included in its modulus and viscosity.
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