We have $$\frac{d^2\theta}{d\hat{t}^2}+\frac{1}{Q}\frac{d\theta}{d\hat{t}} +sin(\theta)=\hat{A}cos(\hat{\omega}\hat{t}).$$ This equation can in turn be recast in terms of two coupled first-order differential equations as follows $$\frac{d\theta}{d\hat{t}}=\hat{v},$$ and $$\frac{d\hat{v}}{d\hat{t}}=-\frac{\hat{v}}{Q}-sin(\theta)+\hat{A}cos(\hat{\omega}\hat{t}).$$ These are the equations to be solved. The factor $Q$ represents the number of oscillations of the undriven system that must occur before its energy is significantly reduced due to the viscous drag. The amplitude $\hat{A}$ is measured in units of the maximum possible gravitational torque while $\hat{\omega}$ is the angular frequency of the external torque measured in units of the pendulum's natural frequency.