# Determine the natural frequencies experimentally

• Mohamed_Wael
In summary, one practical method for determining the system properties of natural frequencies and damping ratio using forced vibration is to measure the phase angle and corresponding exciting frequency on a bode plot. Another approach is to use a forcing mechanism with a displacement sensor, such as a shaker table. If this is not available, a quick and rough method is to excite the system with a known displacement and observe the ring down to calculate the fundamental frequency and damping ratio in the time domain. It is important to clarify the type of system being tested, whether it is a mass spring damper or a motorized system.
Mohamed_Wael
How can we determine the system properties (natural frequencies & damping ratio ) practically using forced vibration?
One way is to measure the phase angle, using the bode plot, the exciting frequency corresponding to 90 (deg) phase shift should be the natural frequency, are there any other approaches using forced vibration as well?

Do you have a forcing mechanism with displacement sensor for the output? (e.g. shaker table?)

If not, a quick and dirty method is to excite the system with a known/repeatable forced displacement, then watch the ring down to calculate the fundamental frequency (counting peaks and calculating period) and damping ratio in the time domain.

Maybe I have interpreted your system wrongly, is this a mass spring damper system, or a motorized system? Maybe describe what it is.

## 1. What is the purpose of determining natural frequencies experimentally?

The purpose of determining natural frequencies experimentally is to accurately understand the dynamic behavior of a system or structure. By identifying the natural frequencies, we can predict how the system will respond to different external forces or vibrations.

## 2. How is the natural frequency of a system measured experimentally?

The natural frequency of a system can be measured experimentally by subjecting the system to a range of different frequencies and measuring the corresponding response of the system. This data can then be used to identify the natural frequencies through various methods such as frequency analysis or modal analysis.

## 3. What are some common methods used to determine natural frequencies experimentally?

Some common methods used to determine natural frequencies experimentally include impact testing, shaker testing, and laser vibrometry. Impact testing involves striking the system with a hammer and measuring the resulting vibrations, while shaker testing uses a controlled vibration source to excite the system. Laser vibrometry uses lasers to measure the vibrations of the system's surface.

## 4. How accurate are experimental methods for determining natural frequencies?

The accuracy of experimental methods for determining natural frequencies depends on several factors such as the type of measurement equipment used, the quality of data collection and analysis, and the complexity of the system being tested. Generally, these methods can provide accurate results within a reasonable margin of error.

## 5. Can natural frequencies change over time?

Yes, natural frequencies can change over time due to several factors such as changes in the system's environment, wear and tear, and structural damage. It is important to regularly reevaluate the natural frequencies of a system to ensure its continued safe and efficient operation.

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