A body of mass $M$ and charge $q$ is connected to spring of spring constant $k.$ It is oscillating along $x$-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 ?
The new equilibrium position is at a distance ${{qE} \over {2k}}$ from $x=0.$
The total energy of the system is ${1 \over 2}m{\omega ^2}{A^2} + {1 \over 2}{{{q^2}{E^2}} \over k}.$
The total energy of the system is ${1 \over 2}m{\omega ^2}{A^2} - {1 \over 2}{{{q^2}{E^2}} \over k}.$
The new equilibrium position is at a distance ${{2qE} \over k}$ from $x=0.$
