Natural Frequency of the Human Body

Written by Kerem Muldur

Objects all around us are able to vibrate with a driving force applied periodically. This motion has several parameters that define its character: its wavelength, frequency, and amplitude— the wavelength is the distance over which the wave's shape repeats, the amplitude is the maximum displacement of the object from its equilibrium position, and frequency is how frequently a wave reaches its amplitude in a second. 

When you pluck a guitar string or push a child on a swing, a back-and-forth motion happens that can be analyzed through these parameters. The amplitude of this vibration depends on the phase and frequency of your power. For example, when you apply the force to a swing that hasn't reached its maximum vertical position, you will have slowed it down instead of adding energy into the system. This phenomenon is called the phase shift. 

A similar principle explains why washing machines sometimes vibrate excessively. Inside the machine, this vibration occurs as the vibration of some parts, such as the drum’s vibration frequency, matches another part’s natural frequency, leading to resonance, the point where every pulse of the other vibration adds energy and increases the amplitude of the vibration.

Natural frequency is the specific level of frequency at which an oscillating object tends to vibrate without a disturbing periodic force. We can easily observe it through daily examples. Imagine you are holding one end of a string attached to a mass at the other end. You move one end of the string back and forth, creating a pendulum. As you increase the amplitude of your pulses, the pendulum would increase its amplitude, and its total energy would increase as a result. The optimum level of the oscillation in terms of amplitude is called the resonance, where the natural frequency of the object matches the driving vibration’s frequency. However, if you increase the pulses per second, your frequency, you would observe that the pendulum takes a shaky, weird shape, rather than smoothly increasing in amplitude. This illustrates how objects in oscillating motion react as you give a driving frequency bigger or smaller than their natural frequency.

Natural frequencies of objects are very crucial for mechanical engineers to design different parts of machines, as they aim to prevent any coincidence between the natural frequencies of interacting parts of machines. For example, the drum of the washing machine’s natural frequency should not match with other parts of the washing machine interacting with it; if it is not prevented, these parts would shake in resonance, a common phenomenon seen in older washing machines. Another good example of this case is cars’ internal parts of their engines, such as the pistons and exhaust manifolds. Whether it is an external effect, such as driving across a bumpy road or a vibration created by a fourth motion of the piston, any effect might cause different parts of the car to vibrate. In the case where the natural frequencies of interacting components of the automobile are really close, even a small vibration might result in a chain of resonance of different body components, directly affecting the parts that interact with the user and passengers, like seats and the steering wheel. 

The experienced comfort of the user and passengers does not only rely on the vibration of the interacting parts, it is also directly associated with how close these parts’ natural frequencies are to the natural frequency of the human body. 

Just like washing machines have drums and automobiles' exhaust manifolds, our bodies and their specific parts tend to resonate at a specific frequency, called the natural frequency of the human body. This is very crucial in designing the steering wheel and seats to not align with the parts that interact with it, like preventing the steering wheel’s natural frequency from being close to the natural frequency of the hands. 

To calculate the natural frequency of the human body and different parts, researchers from Minas Gerais imagined the human body as a mass attached to a spring, and used several people of different ages, sexes, body mass index, vision, and posture.

To calculate each person’s natural frequency, the volunteers were placed on a metal chair that was vibrated through a frequency varying from 16hz to 80hz. An acceleration sensor is placed at the center point of the metal surface. Then, the volunteers were informed to let the researchers know at the points where the vibration is detectable, called the perception threshold, and when the vibration level is unbearable, called the maximum acceptable vibration. Let’s take a look at the findings of the research about what parameters affect the natural frequency and what the values are for different frequencies for different body parts.

Age

Older subjects reacted later for the perception threshold and maximum acceptable threshold than the younger subjects. This is associated with the increase in the damping effect of soft tissues on the body and a decrease in sensory perception.

Vision

Researchers assumed that closed eyes would heighten the sensitivity. Contrasting to the hypothesis for the sex case, they were right. Even though the effect was not too strong overall, the volunteers reacted earlier to the perception threshold, meaning they felt the vibrations more easily.

Posture

Another finding of the research was that standing vs sitting changes which body parts dominate the resonance. The main difference is caused by the load distribution of the body parts, where, for the standing posture, leg muscles carry a bigger percentage when the user is not seated.

Natural frequency of the human body is not only a numerical value, it is a key variable for the designers building any machine interacting with the human body. Just as engineers must prevent the natural frequencies of mechanical parts from coinciding to avoid damaging vibrations, designers of vehicles, chairs, and tools must consider how their products interact with the natural frequencies of the human body. The findings from studies, such as the one conducted in Minas Gerais, demonstrate that factors like age, posture, and sensory conditions influence how we perceive and tolerate vibration.

Understanding these natural frequencies is crucial for ensuring both safety and comfort. In automobiles, it can mean the difference between a smooth ride and one that causes fatigue or even health risks. In occupational environments, it can determine how long a person can safely operate vibrating machinery. Ultimately, recognizing the resonance of the human body reminds us that we are not separate from the physical laws that govern the world around us, but participants in them—living systems that resonate just like strings, pendulums, and machines.

The psychology behind unethical behavior is multifaceted, shaped by cognitive processes, situational pressures, social influence, and self-interest. By studying these psychological mechanisms, we gain insights into why people sometimes act against their moral beliefs. Recognizing these factors can equip individuals and organizations with tools to foster ethical behavior, allowing us to address unethical behavior effectively and cultivate a more conscientious and ethical society.

References:

1. Duarte, Maria Lucia & Pereira, Matheus. (2006). Vision Influence on Whole-Body Human Vibration Comfort Levels. Shock and Vibration. 13. 367-377. 10.1155/2006/950682.

2. What is resonance? (2024, 8). GAMAK. https://www.gamak.com/en/delving-into-resonance-causes-and-negative-implications

3. Ren, W. (2018, February 7). Study on Vibration Characteristics and Human Riding Comfort of a Special Equipment Cab. https://onlinelibrary.wiley.com/. https://onlinelibrary.wiley.com/doi/10.1155/2018/7140610