Mathematical Methods: Oscillations and Energy Transfer

This lecture covers mathematical methods for physicists, focusing on oscillations and energy transfer in systems involving springs and external forces. The instructor begins by reviewing concepts from the previous lecture, discussing the collision of two balls and the resulting velocities. The discussion transitions to the analysis of a mass attached to a spring, subjected to an external force over a defined time interval. The instructor derives the amplitude of oscillation after the external force ceases, emphasizing the importance of energy and momentum conservation in evaluating the results. The lecture introduces the concept of the Green function as a tool for solving linear differential equations with sources, demonstrating how to compute the response of the system to a delta function input. The final part of the lecture presents the integral formulation for the amplitude of oscillation, illustrating how the system behaves after the external force is removed. The instructor encourages students to engage with the material and apply these concepts in exercises.