A particle of unit mass subjected to the 1-dimensional potential
\(V(x)=\frac{2 α}{x^3}-\frac{3 β}{x^2}\)
executes small oscillations about its equilibrium position, where α and β are positive constants with appropriate dimensions. The time period of small oscillations is
1
\(\frac{\pi \alpha^2}{\sqrt{6 \beta^5}}\)
2
\(\frac{\pi \alpha^2}{\sqrt{3 \beta^5}}\)
3
\(\frac{2 \pi \alpha^2}{\sqrt{3 \beta^5}}\)
4
\(\frac{2 \pi \alpha^2}{\sqrt{6 \beta^5}}\)