Why is natural frequency important?

Hint:One definition unites the terms "nature" and "natural": "being in or originated by nature; not made or impacted by people." This concept is simple and direct, but it also encompasses a wide range of occurrences from which we, as humans, draw inspiration to advance both the field of electronics and science in general.
Frequency is one such naturally occurring phenomenon that affects a variety of industries, including electronics. We commonly speak of natural frequency when discussing electronic equipment and systems, which may be computed using the natural frequency formula.

Complete step by step solution:
Natural frequency important:
In the absence of any driving force, the system's natural frequency is the frequency at which it tends to oscillate. When an object vibrates at a frequency that is equal to its natural frequency, the amplitude of the vibration increases dramatically, potentially causing irreversible damage; therefore, knowing the natural frequency is critical.
Natural frequencies and mode shapes are often regarded as the single most important properties of practically any system. Excessive vibrations in any system, as you might expect, cause structural and functional problems.
The reason for this is that natural frequencies might match resonant frequencies in a system. If you apply a time-varying force to a system and choose a frequency that is equivalent to one of the natural frequencies, massive amplitude vibrations will follow, putting your system at risk.
This is why, when constructing a mechanical system, it's critical to calculate and verify that the natural frequencies of vibration are significantly greater than any probable excitation frequency.

Note:Natural Frequency Shifting Techniques:
The following are general rules for allowing natural frequency shifting and limiting a system's vibrational response:
Increase the stiffness to increase the natural frequency.
Increase the bulk to lower the natural frequency.
The peak response is reduced as the damping is increased, while the response range is broadened.
The peak response is increased when the damping is reduced, but the response range is narrowed.
The response at the resonance frequency is mitigated by lowering the driving amplitudes.
The natural frequency value is one of a system's most important metrics or attributes. The importance of designers being aware of the correct frequency point is critical to the functionality, performance, and life cycle of a system.