Two degree of freedom damped free vibration refers to a type of vibration in which a mechanical system with two degrees of freedom (two independent modes of motion) is subject to damping, or the dissipation of energy, without any external forces acting on it.
The damping coefficient in a two degree of freedom damped free vibration system is typically calculated using the logarithmic decrement method. This involves measuring the amplitude of the system's vibrations at two different points in time and using a formula to determine the damping ratio, which is then used to calculate the damping coefficient.
The natural frequencies in a two degree of freedom damped free vibration system represent the frequencies at which the system will vibrate with the greatest amplitude in the absence of damping. These frequencies are determined by the system's mass, stiffness, and damping coefficients, and can be used to analyze and predict the behavior of the system.
Damping in a two degree of freedom damped free vibration system reduces the amplitude of the vibrations over time, eventually causing the system to reach a state of equilibrium and stop vibrating. It also affects the natural frequencies of the system, with higher damping resulting in lower natural frequencies and thus a slower rate of vibration.
Two degree of freedom damped free vibration systems have numerous applications in engineering and science, including in mechanical systems such as bridges, buildings, and vehicles. They are also used in the study of earthquakes and structural dynamics, as well as in the design of musical instruments and shock absorbers.