5. A simple model of a viscoelastic material consists of a spring of modulus E in parallel with a dashpot of viscosity 7, with a stress-strain relation o(t) = Ee + nde/dt. (a) Assuming a harmonic strain of the form e(t) Egexp(iwt), derive an expression for the complex modulus E*(w) = E+iE2. (b) A constant stress oo is applied to the undeformed state at t = 0. Derive an expression for the strain as a function of time and discuss the short- and long-time limits (Hint: you will have to solve a differential equation).

5. A simple model of a viscoelastic material consists of a spring of modulus E in parallel with a dashpot of viscosity 7, with a stress-strain relation o(t) = Ee + nde/dt. (a) Assuming a harmonic strain of the form e(t) Egexp(iwt), derive an expression for the complex modulus E*(w) = E+iE2. (b) A constant stress oo is applied to the undeformed state at t = 0. Derive an expression for the strain as a function of time and discuss the short- and long-time limits (Hint: you will have to solve a differential equation).