Vibrations and Waves Problem Solving

General discussion of electromagnetic fields produced by moving charges, in particular by charges that accelerate.

In this session, we show how the properties (wavelength, frequency, amplitude and polarization) of an electromagnetic wave can be concluded from the equation that describes the wave and vice versa.

Consideration of the interference of electromagnetic waves produced by multiple oscillating charges, and the fields produced at distances from the charges where all other fields can be ignored and the rays from every charge are approximated as parallel.

In this session, we extend the solution of the motion of oscillators with one degree of freedom without damping to the case where damping can no longer be ignored.

Discussion of systems with infinite number of degrees of freedom, in particular where the oscillators are identical, harmonic, and connected only to their neighbors. Examples include a taut string and a transmission line (two parallel conductors).

First, advice on how, in general, one approaches the solving of "physics problems." Then three very different oscillating systems, and how in each the equations of motion can be derived and solved to obtain the motion of the oscillator.

In this session, we solve problems involving harmonic oscillators with several degrees of freedom ̶ i.e., several discreet oscillators which are coupled or interconnected to each other. Only systems where damping can be ignored are considered.

In this session, we do more standing wave problems. The focus is on the role of boundary conditions at the intersection of two continuous media with different physical characteristics.

Continued discussion of systems with infinite degrees of freedom, where oscillators are identical, harmonic, connected only to their neighbors, and the solution to the wave equation is described as the superposition of normal modes (Fourier analysis).

We discuss the role problem solving plays in the scientific method. Then we focus on problems of simple harmonic motion ̶ harmonic oscillators with one degree of freedom in which damping (frictional or drag) forces can be ignored.