Problem $3$: Viscoelastic Behavior

Consider a visco$-$elastic material whose behavior is adequately described by the Zener model $($combined series$-$parallel model$).$ Let the time interval, $\backslash (\backslash$Delta $\backslash$mathrm$\{$t$\}=\backslash$mathrm$\{$K$\}\_\{\backslash$mathrm$\{$v$\}\}/\backslash$mathrm$\{$K$\}\_\{\backslash$mathrm$\{$e$\}2\}=\backslash$tau$\_\{\backslash$mathrm$\{$e$\}\}\backslash ),$ and assume $\backslash (\backslash$mathrm$\{$K$\}\_\{\backslash$mathrm$\{$e$\}1\}=\backslash$mathrm$\{$K$\}\_\{\backslash$mathrm$\{$e$\}2\}\backslash ).$

a$)$ Given the force vs$.$ time history shown below, where there is a period of tension followed by compression and tension again. After that, the stress is $0.$ Sketch as the corresponding variation of strain with time.

b$)$ Given the strain vs$.$ time history shown below, where there is a period of tension followed by compression and tension again. Sketch the corresponding variation of force with time.