This paper investigates the transient response of a
dynamical system modelling an automatic dynamic balancing
mechanism for eccentric rotors. This approach allows one
to quantify which
eigenvalues are most sensitive to
perturbation. It is shown how the sensitivity of the
eigenvalues directly influences the transient response.
Furthermore, the effect which a
variation of the damping
coefficients has on the pseudospectra structure is
considered. A transient growth due to the non-normality of
the linearised system is shown to lead to an exponential
decay or to a collapse back to the stable equilibrium;
these effects are identified with the changes in the
sensitivities of the eigenvalues under variation of the
damping parameters. This provides a new insight into the
full nonlinear system, in which qualitatively similar
transient responses are shown to occur.