  Dynamic response of the one-dimensional viscoelastic rod of finite length,
that has one end fixed and the other subject to prescribed either displacement
or stress, is analyzed by the analytical means of Laplace transform, yielding
the displacement and stress of an arbitrary rod's point as a convolution of the
boundary forcing and solution kernel. Thermodynamically consistent Burgers
models are adopted as the constitutive equations describing mechanical
properties of the rod. Short-time asymptotics implies the finite wave
propagation speed in the case of the second class models, contrary to the case
of the first class models. Moreover, Burgers model of the first class yield
quite classical shapes of displacement and stress time profiles resulting from
the boundary forcing assumed as the Heaviside function, while model of the
second class yield responses that resemble to the sequence of excitation and
relaxation processes.
