What happens to natural frequency if the mass of the machine is increased?

When considering the relationship between mass and natural frequency in mechanical systems, it's essential to understand how these parameters interact. The natural frequency of a system is inversely related to the square root of the mass. This is expressed in the formula for natural frequency:

[ f_n = \frac{1}{2\pi} \sqrt{\frac{k}{m}} ]

where ( f_n ) is the natural frequency, ( k ) is the stiffness of the system, and ( m ) is the mass. An increase in mass results in a higher denominator when calculating the natural frequency, leading to a decrease in the natural frequency value.

In the context of amplitude, while natural frequency decreases as the mass increases, this modification can influence the system's response to external forces or vibrations. However, it is important to note that simply increasing the mass does not inherently cause the amplitude to change. The amplitude of a vibrating system is influenced by other factors such as excitation forces, damping, and system stiffness, rather than just the mass itself.

Therefore, when the mass is increased, the natural frequency decreases while the amplitude remains unchanged under the specific condition of no additional external influences being applied. This understanding is integral to vibration analysis and helps predict the behavior