nasu said:Have you tried to google the topic? Or even look it up in a book?
The volume on waves from the famous Berkley course (volume 3 of 5) has an excellent discussion of these topics.
Look up Waves by Crawford, for the reference.
A free damped vibration is a type of oscillation that occurs in a system with two degrees of freedom, where the motion of each degree of freedom is affected by both a damping force and a restoring force.
The free damped vibration of a 2 dof system can be demonstrated using a physical model or through mathematical analysis using equations of motion.
The damping coefficient, stiffness of the system, and initial conditions (such as initial displacement and velocity) can all affect the free damped vibration of a 2 dof system.
Damping can reduce the amplitude and change the frequency of the vibrations in a 2 dof system. Higher damping coefficients result in faster decay of the vibrations.
Some real-world applications of free damped vibration of 2 dof systems include shock absorbers in vehicles, earthquake-resistant structures, and machinery with moving parts that require precise control of vibrations.