What is meant by natural vibration?

Hint: In the absence of any driving or damping force, a system's natural frequency, also known as eigen frequency, is the frequency at which it tends to oscillate. The normal mode is the motion pattern of a system vibrating at its inherent frequency. The resonant frequency is the frequency at which an oscillating system is pushed by an external force at the frequency at which the amplitude of its motion is highest.

Complete answer:
Natural vibrations are free vibrations of an elastic body that occur at a frequency termed the natural frequency. Forced vibrations, which occur at the frequency of an applied force, vary from natural vibrations (forced frequency). When the forced frequency is equal to the natural frequency, the amplitude of the vibrations rises by a factor of ten. Resonance is the term for this phenomena.
The natural frequency of a mass-spring system with mass m and spring stiffness k may be computed as follows:
\[{{\omega }_{0}}=\sqrt{\dfrac{k}{m}}\]
In the absence of dampening or a driving force, the natural frequency of an item is its vibration frequency. The body's free vibration, or natural vibration, occurs at the natural frequency. When there is no external force acting on the body and the movement of the object is mostly due to the object's original displacement, the phrase "free vibration" is employed. In the absence of any driving or damping force, a body's natural frequency is the frequency at which it tends to oscillate.
Natural vibrations are free vibrations of any elastic body that occur at a frequency termed natural frequency. Forced vibrations, which occur at the frequency of the applied force, vary from natural vibrations.

Note:
When a material oscillates at a high amplitude at a certain frequency, it is said to be in resonance. This frequency is referred to as resonant frequency. “The state of a system in which an unusually big vibration is created in response to an external stimulus, happening when the stimulus frequency is the same, or nearly the same, as the system's natural vibration frequency,” according to the dictionary.