At the equilibrium position of a particle executing SHM

 $$\begin{gathered} Force=F = -kx \\ k is force cons\tan t \\ x is displacement \\ at x=0,Force = -k\left(0\right) \\ F=0 \end{gathered}$$

$$\begin{gathered} velocity of particle,v=\omega \sqrt[ ]{\left(A^2-x^2\right)} \\ {v}^2={\omega }^2\left(A^2-x^2\right) \\ at x=0, Kinetic energy of particle =\frac{1}{2}m{\omega }^2\left(A^2-0^2\right)= maximum \\ PE=\frac{1}{2}m{\omega }^2\left(x^2\right) \\ at x=0, PE=0 \end{gathered}$$                                      

          Potential energy=PE=minimum