A mass attached to a spring is free to oscillate, with angular velocity \(\omega\), in a horizontal plane without friction or damping. It is pulled to a distance${}_{}$ \(x_0\) and pushed towards the centre with a velocity \(v_0\) at time \(t=0\). The amplitude of the resulting oscillations is:
1. \(\sqrt{\left(2x_0^2+\frac{v_0^2}{\omega^2}\right)} \)
2. \(\sqrt{\left(x_0^2+\frac{v_0^2}{\omega^2}\right)} \)
3. \(\sqrt{\left(x_0^2+\frac{v_0^2}{2\omega^2}\right)} \)
4. \(\sqrt{\left( x_0^2+\frac{v_0^2}{\pi\omega^2}\right)} \)