The solution for a particular mode is of the form
$$u_i(x,t) = w_i(x)\sin(\omega_i t + \phi)$$
where $w_i(x)$ is the $i$th eigenfunction and $\omega_i$ the $i$th eigenvalue, $\phi$ is a phase and, we can assume $\phi=0$. Then, the solution for the mode is
$$u_i(x,t) = w_i(x)\sin(\omega_i t) \enspace .$$
Thus, you can present your mode as an animation changing the amplitude proportionally to the sine function presented. In commercial software it is common to have the option to vary $t \in [0,\pi]$ and $t \in [0,2\pi]$, and they are termed half cycle or full cycle (or half harmonic and full harmonic).
The correct thing to do is to animate over the full range $[0,2\pi]$, but since the amplitude will be the same (but opposite sign) in the other half some people do not consider it necessary.