Average velocity of a particle executing SHM in one complete vibration is

The average velocity of a particle executing simple harmonic motion (SHM) is

                          ${\mathrm{\nu }}_{\mathrm{av}}=\frac{\text{ Total displacement }}{\text{ Time interval }}=\frac{{\mathrm{x}}_{\mathrm{f}}-{\mathrm{x}}_{\mathrm{i}}}{\mathrm{T}}$

where, x_f and x_i are the initial and final position of the particle executing SHM.
As in SHM, the particle executes motion about its mean position. So, after one complete oscillation by the particle, it will reaches its initial position, i.e.

Displacement, ${\mathrm{x}}_{\mathrm{f}}-{\mathrm{x}}_{\mathrm{i}} = 0$

$\therefore {\mathrm{v}}_{\mathrm{av}}=\frac{0}{\mathrm{T}}$

Hence, the average velocity is zero.