  NGC 5194 (M51a) is a grand-design spiral galaxy and undergoing interactions
with its companion. Here we focus on investigating main properties of its
star-formation history (SFH) by constructing a simple evolution model, which
assumes that the disc builds up gradually by cold gas infall and the gas infall
rate can be parameterizedly described by a Gaussian form. By comparing model
predictions with the observed data, we discuss the probable range for free
parameter in the model and then know more about the main properties of the
evolution and SFH of M51a. We find that the model predictions are very
sensitive to the free parameter and the model adopting a constant infall-peak
time $t_{\rm p}\,=\,7.0{\rm Gyr}$ can reproduce most of the observed
constraints of M51a. Although our model does not assume the gas infall
time-scale of the inner disc is shorter than that of the outer disc, our model
predictions still show that the disc of M51a forms inside-out. We find that the
mean stellar age of M51a is younger than that of the Milky Way, but older than
that of the gas-rich disc galaxy UGC 8802. In this paper, we also introduce a
'toy' model to allow an additional cold gas infall occurred recently to imitate
the influence of the interaction between M51a and its companion. Our results
show that the current molecular gas surface density, the SFR and the UV-band
surface brightness are important quantities to trace the effects of recent
interaction on galactic SF process.
