dwsmith said:Does anyone know where I find second order damped wave equation worked where the overdamped, underdamped, and critically damped cases are all taken into account?
I found resources where they throughout the overdamped and just focus on the underdamped.
Sudharaka said:Hi dwsmith, :)
Are you trying to find an article where all the cases; over-damping, under-damping and critical damping are described? Then the following lecture note from MIT OpenCourseWare may help you.
http://ocw.mit.edu/courses/mathemat...monic-oscillators/MIT18_03SCF11_s13_2text.pdf
Kind Regards,
Sudharaka.
The wave equation is a mathematical formula that describes the behavior of waves in various physical systems, such as sound waves, light waves, and water waves. It relates the wave's amplitude, wavelength, and frequency to its speed and the medium through which it is traveling.
The wave equation is used in many fields, including physics, engineering, acoustics, and seismology. It can be used to analyze and predict the behavior of waves in different systems, such as electromagnetic waves in telecommunication, sound waves in musical instruments, and seismic waves in earthquake studies.
The wave equation is derived from fundamental principles of physics, such as Newton's laws of motion and the conservation of energy. It can also be derived using advanced mathematical techniques, such as partial differential equations and Fourier analysis.
The wave equation is a simplified model and does not account for all factors that may affect wave behavior, such as viscosity and turbulence in fluids. It also assumes a linear medium, where the wave's amplitude does not significantly affect its speed or direction. In reality, these factors may play a role in the wave's behavior.
The wave equation is a fundamental tool in many areas of scientific research. It is used to study the properties of waves and their interactions with different mediums. It is also used in the development of new technologies, such as medical imaging techniques and earthquake prediction methods.