  A parametric oscillator with damping driven by white noise is studied. The
mean square displacement (MSD) in the long-time limit is derived analytically
for the case that the static force vanishes, which was not treated in the past
work \cite{tashiro07}. The formula is asymptotic but is applicable to a general
periodic function. On the basis of this formula, some periodic functions
reducing MSD remarkably are proposed.
