A \(3.42\,\text{kg}\) stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where \(g = 9.80\,\text{m/s}^2\). If the force constant (spring constant) of the spring is \(12\,\text{N/m}\), find the period of oscillation of this setup on a planet where \(g = 1.60\,\text{m/s}^2\).