A linear molecule is modelled as two atoms of equal mass m placed at coordinates x1 and x2, connected by a spring of spring constant k. The molecule is moving in one dimension under an additional external potential \(V\left(x_1, x_2\right)=\frac{1}{2} m ω_0^2\left(x_1^2+x_2^2\right)\). If one frequency of molecular vibration is ω0, the other frequency is
1
\(\sqrt{ω_0^2-\frac{k}{m}}\)
2
\(\sqrt{ω_0^2+\frac{k}{m}}\)
3
\(\sqrt{ω_0^2+\frac{2 k}{m}}\)
4
\(\sqrt{ω_0^2-\frac{2 k}{m}}\)