<p>This study presents parametric resonance in a damped coplanar double pendulum driven by pivot vibration or gravity modulation. These two driving methods yield qualitatively identical results, aside from a phase difference when the two masses of the pendulum are equal. In contrast, for unequal masses, the solutions differ significantly for large values of the driving parameters. In the absence of driving and damping, the general form of normal mode frequencies is calculated. Special conditions are derived when the equations of motion for each one of the two pendula become identical. The dynamics of the parametrically forced pendulum are analysed by determining the Floquet multipliers. A double pendulum has four Floquet multipliers, organised into two sets. Each set comprises two real numbers or a complex conjugate pair. Each set of real negative Floquet multipliers correspond to subharmonic oscillations with a period twice that of the driving force, while real positive multipliers indicate harmonic oscillations synchronous with the driving. The complex multipliers relate to the decaying motion of the pendulum.</p>