A stationary wave of amplitude $\mathrm{A}$ is generated between the two fixed ends $\mathrm{x}=0$ and $\mathrm{x}=\mathrm{L}$. The particle at $\mathrm{x}=\frac{\mathrm{L}}{3}$ is a node. There are only two particles between $\mathrm{x}=\frac{\mathrm{L}}{6}$ and $\mathrm{x}=\frac{\mathrm{L}}{3}$ which have maximum speed half of the maximum speed of the anti-node. Again there are only two particles between $\mathrm{x}=0$ and $\mathrm{x}=\frac{\mathrm{L}}{6}$ which have maximum speed half of that at the antinodes. The slope of the wave function at $\mathrm{x}=\frac{\mathrm{L}}{3}$ changes with respect to time according to the graph shown. The symbols $\mathrm{\mu }$, $\mathrm{\omega }$ and $\mathrm{A}$ are having their usual meanings if used in calculations.



The time period of oscillations of a particle is