Resonance oscillation of a damped driven simple pendulum

The resonance characteristics of a driven damped harmonic oscillator are well known. Unlike harmonic oscillators which are guided by parabolic potentials, a simple pendulum oscillates under sinusoidal potentials. The problem of an undamped pendulum has been investigated to a great extent. However, the resonance characteristics of a driven damped pendulum have not been reported so far due to the difficulty in solving the problem analytically. In the present work we report the resonance characteristics of a driven damped pendulum calculated numerically. The results are compared with the resonance characteristics of a damped driven harmonic oscillator and also with those of a damped driven Duffing oscillator. The work can be of pedagogic interest too as it reveals the richness of driven damped motion of a simple pendulum in comparison to, and how strikingly it differs from, the motion of a driven damped harmonic oscillator. We confine our work only to the nonchaotic regime of pendulum motion.