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 $$ \hat{A}=\frac{A}{mg} $$