One-Dimensional Wave Equations

This course covers the comprehensive understanding of one-dimensional wave equations. It begins with the derivation of the wave equation using three different approaches: the discrete approach, the continuum approach using Newton's second law, and Hamilton's equation. The course then delves into the concept of transverse vibration of a string and its role in studying wave propagation. It further discusses the general solution of the wave equation, representing the superimposition of two functions, indicating waves traveling in opposite directions. The course also explains how wave velocity depends on the tension in the string and the material density. It concludes with a detailed analysis of forced vibration analysis of a string, incorporating the effect of damping and the modal superposition technique. The course uses the example of a string subjected to different types of forces, such as a step input and harmonic excitation, to illustrate the concepts.