 Solution

On a timescale short compared with $\tau =\eta /E$, or for $\omega \tau \gg 1$, the dashpot strongly resists rapid deformation. The imposed oscillating stress produces a small strain, of amplitude approximately ${\sigma }_0/(\eta \omega )$, nearly90degrees behind the stress. The network appears stiff and predominantly viscous in this stress-controlled high-frequency limit. It is not an ideal perfectly rigid body at finite frequency.