Let a viscoelastic material be modeled by a chain of $3$ Kelvin solids in series of the following figure:

$\backslash$sigma $([$E$1$ spring F$1$ dumper$]$ in parallel$)([$E$2$ spring F$2$ dumper$]$ in parallel$)([$E$3$ spring F$3$ dumper$]$ in parallel$)->\backslash$sigma

Let q be a $\backslash$sigma $-$dimensional constant, T another time$-$dimensional constant, and:

E$1=2$q; F$1=2$qT

E$2=$q; F$2=4$qT$$

E$3=1\mathrm{.}5$q; F$3=16\mathrm{.}5$qT

$1-$Determine the differential equation for the material's behavior.

$2-$Use the Laplace transformation to find the material's creep compliance.

$3-$Graph $\backslash$epsi $($t$)$ for the following excitation cases:

$3$a$)\backslash$sigma $=\backslash$sigma $0(\backslash$Delta $($t$)-\backslash$Delta $($t$-0\mathrm{.}8$T$))$

$3$b$)\backslash$sigma $=\backslash$sigma $0(\backslash$Delta $($t$)-\backslash$Delta $($t$-3\mathrm{.}0$T$))$

$4-$Determine analytically the preponderance of each of the chain's solids $1,2,$ and $3$ in relation to the$$

whole solids' system, and graph this using the response to excitation in each of cases $3$a and $3$b$.$