We define $$\omega_0=\sqrt{g/l},$$ the so-called natural frequency and the new dimensionless quantities $$\hat{t}=\omega_0t,$$ with the dimensionless driving frequency $$\hat{\omega}=\frac{\omega}{\omega_0},$$ and introducing the quantity $Q$, called the quality factor, $$Q=\frac{mg}{\omega_0\nu},$$ and the dimensionless amplitude $$\hat{A}=\frac{A}{mg}$$