  We investigate theoretical aspects of the detection of Majorana bound states
in Josephson junctions using the semiclassical RCSJ model of junction dynamics.
The influence of a 4$\pi$-periodic supercurrent contribution can be detected
through its effect on the width of the Shapiro steps and the Fourier spectrum
of the voltage signal. We explain how the inclusion of a capacitance term
results in a strong quenching of the odd steps when the junction is
underdamped, and hence may be used to effectively detect Majorana bound states.
Furthermore, in presence of capacitance the first and third steps are quenched
to a different degree, as observed experimentally. We examine the emission
spectrum of phase-locked solutions, showing that the presence of
period-doubling may difficult the measurement of the 4$\pi$-periodic
contribution from the Fourier spectrum. Finally, we study the voltage response
in the quasiperiodic regime and indicate how the Fourier spectra and the
first-return maps in this regime reflect the change of periodicity in the
supercurrent.
