A particle moves such that its acceleration is given by : a =$-\beta \left(x-2\right)$  Here  $\beta$ is a positive constant and x the position from origin. Time period of oscillations is 

a = o at x = 2 i.e. x = 2 is the mean position. 

                        Assuming      x – 2 = X

                                                a =  $-\beta X$        i.e. $a\infty - X$ ;        a=$-{\omega }^{2}X$

         ${\omega }^2=\beta T=\frac{2\pi }{\omega } =\frac{2\pi }{\sqrt{\beta }}$