# Equivalent Mass Calculator

## About Equivalent Mass Calculator (Formula)

An Equivalent Mass Calculator is a tool used to determine the equivalent mass of a mechanical system that experiences vibration or oscillation due to a force or disturbance. Equivalent mass is a concept used in mechanical engineering to simplify the analysis of complex systems by representing them as a single mass that would yield the same response under the same conditions.

The formula for calculating equivalent mass can vary depending on the specific system and the nature of the excitation force. However, a common formula for a single-degree-of-freedom system subjected to harmonic excitation is:

Equivalent Mass (m_eq) = m / (1 – (ω^2 / ω_n^2))

Where:

• Equivalent Mass (m_eq) is the mass that would yield the same response as the original system.
• m is the actual mass of the system.
• ω is the angular frequency of the excitation force.
• ω_n is the natural angular frequency of the system.

To use the Equivalent Mass Calculator formula, follow these steps:

1. Determine the actual mass of the system (m).
2. Determine the angular frequency of the excitation force (ω). This is calculated as 2π times the frequency of the force (ω = 2πf).
3. Determine the natural angular frequency of the system (ω_n). This is a characteristic frequency of the system that depends on its properties.
4. Plug the values of actual mass (m), angular frequency of the excitation force (ω), and natural angular frequency of the system (ω_n) into the formula: Equivalent Mass (m_eq) = m / (1 – (ω^2 / ω_n^2)).
5. Calculate the equivalent mass (m_eq) that simplifies the analysis of the system’s response.

Equivalent mass is a valuable concept in engineering, especially in the analysis and design of mechanical systems subjected to vibrations. It allows engineers to model complex systems as simpler single-degree-of-freedom systems, making calculations and predictions more manageable.

Keep in mind that equivalent mass calculations can become more complex for systems with multiple degrees of freedom or when considering other factors like damping.