Part C only, treat it as an ode with initial condition T(t=0) = 0 to find T(t). And then use integrate by part to show that it can be expressed in the integral form.

(b) Show that the continuum version of the result from part (a) has the form aT DE 22 E T + TO at = T1 at + T 2 at 2 ' where the Ti's are positive with TOT1 > T2. (c) Show that the viscoelastic constitutive law in part (b) can be expressed in integral form as T = kie' + G (t - s)E' (s) ds, where G ( t ) = kze-t/ x Assume that e = c' = 0 and T = 0 at t = 0. Also, show that ki's and 1 are positive