Potential energy of the particle is

$V(x)=-\alpha x+\beta \sin \left(\frac{x}{\gamma}\right)$

Clearly, dimensions of $\alpha, \beta$ and $\gamma$ are

$[\alpha]=\frac{[ V ]}{[ x ]}=\frac{\left[ ML ^2 T ^{-2}\right]}{[ L ]}=\left[ MLT ^{-2}\right]$

$\mid \beta]=[ V ]=\left[ ML ^2 T ^{-2}\right]$

and $[\gamma]=[ x ]=[ L ]$

$=\left[ M ^0 L ^0 T ^0\right]$