Past exam of the quantum condensed matter course of the University of Cambridge / 2008 / Section A / A3 / b

The Maxwell model has a spring of modulus $G_0$ in series with a dashpot of viscosity $\eta$. Their stresses are equal and strains add, giving $\dot{\gamma }=\dot{\sigma }/G_0+\sigma /\eta$. After a step strain ${\gamma }_0$, the strain rate is zero for $t>0$, so $\dot{\sigma }=-\sigma /\tau$ with $\tau =\eta /G_0$. Initially the spring takes the step, $\sigma (0^{+})=G_0{\gamma }_0$. Hence