Given the following model:

a$.$ Determine the mathematical governing equations for the system using the Laplace

transform.

b$.$ Given a constant stress, $(t)={}_0$ and an initial condition, $=0($No strain$)$ at $t=0,$

determine the equation that describes the creep behavior of the system.

c$.$ One study performed mechanical testing of porcine $($pig$)$ cardiac tissue in an environment

similar in cell density to that of the porcine heart. It was subsequently found that $E_1$~~$8\mathrm{.}5$

$M\frac{N}{m^2},E_2$~~$11$MPa,$=1\mathrm{.}3$GPa$*s.$ Predict the creep response, $(t),$ of the porcine cells

when subjected to a stress, ${}_0=100$kPa.