Forced Oscillators and Coupled Systems

This lecture covers the concepts of forced oscillators and coupled systems. It starts by explaining the linear harmonic oscillator and its forced version, detailing the equations of motion and solutions. The lecture then explores the analogy between mechanical and electrical oscillators, discussing energy analysis and resonance. It delves into the synchronization of coupled oscillators, illustrating examples like Huygens' discovery of synchronization in pendulum clocks. The application of coupled oscillators in real-life scenarios, such as the Taipei 101 tower's damping system, is also discussed. The lecture concludes with a detailed analysis of harmonic oscillators coupled through springs, examining their modes of motion and energy distribution.