Final answer:
The natural frequency is the frequency at which a system oscillates without any driving or damping forces, while the damped frequency is the frequency at which a system oscillates when it is affected by damping forces.
Step-by-step explanation:
The major difference between the natural frequency and the damped frequency of oscillation is that the natural frequency is the frequency at which a system will oscillate if not affected by driving or damping forces, while the damped frequency is the frequency at which a system oscillates when it is affected by damping forces. The natural frequency is determined by the system's characteristics, such as mass and stiffness, while the damped frequency depends on the amount of damping present in the system.
For example, consider a simple pendulum. The natural frequency of the pendulum is determined by its length and the acceleration due to gravity, and it will oscillate at this frequency if there is no damping. However, if the pendulum is subject to air resistance or friction, it will experience damping, and the frequency of oscillation will be different from the natural frequency.
In summary, the natural frequency is the inherent frequency of a system, while the damped frequency is the frequency at which a system oscillates when affected by damping forces.