$A$ body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along the $x-$ direction about its equilibrium position,taken to be at $x = 0$,with an amplitude $A$. An electric field $E$ is applied along the $x-$ direction. Which of the following statements is correct?

• A
  The total energy of the system is $\frac{1}{2} M \omega^2 A^2 + \frac{1}{2} \frac{q^2 E^2}{k}$
• B
  The new equilibrium position is at a distance: $\frac{2qE}{k}$ from $x = 0$
• C
  The new equilibrium position is at a distance: $\frac{qE}{2k}$ from $x = 0$
• D
  The total energy of the system is $\frac{1}{2} M \omega^2 A^2 - \frac{1}{2} \frac{q^2 E^2}{k}$