Frequency Of Vibration Calculator

Frequency of Vibration Formula:

\[ v_{vib} = \frac{1}{2\pi} \times \sqrt{\frac{k_1}{m}} \]

Vibrational Frequency (vᵥᵢᵦ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Frequency of Vibration Formula?

The frequency of vibration formula calculates the natural frequency of a spring-mass system. It represents how many oscillations occur per second when the system is displaced from its equilibrium position and released.

2. How Does the Calculator Work?

The calculator uses the frequency of vibration formula:

\[ v_{vib} = \frac{1}{2\pi} \times \sqrt{\frac{k_1}{m}} \]

Where:

\( v_{vib} \) — Vibrational frequency (Hz)
\( k_1 \) — Spring stiffness (N/m)
\( m \) — Mass (kg)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula shows that vibrational frequency increases with higher spring stiffness and decreases with larger mass. The square root relationship indicates that frequency is proportional to the square root of the stiffness-to-mass ratio.

3. Importance of Vibrational Frequency Calculation

Details: Calculating vibrational frequency is crucial for designing mechanical systems, analyzing structural dynamics, preventing resonance in engineering applications, and understanding oscillatory behavior in physical systems.

4. Using the Calculator

Tips: Enter spring stiffness in Newtons per meter (N/m) and mass in kilograms (kg). Both values must be positive numbers greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for input values?
A: Spring stiffness should be in Newtons per meter (N/m) and mass should be in kilograms (kg) for accurate results in Hertz (Hz).

Q2: Does this formula work for all types of springs?
A: This formula applies to ideal linear springs following Hooke's law. For non-linear springs or complex systems, additional factors may need consideration.

Q3: What is the significance of the 2π factor?
A: The 2π factor converts from angular frequency (radians per second) to linear frequency (cycles per second or Hertz).

Q4: How does damping affect the vibrational frequency?
A: This formula calculates the natural frequency without damping. With damping, the actual frequency may be slightly lower than the natural frequency.

Q5: Can this formula be used for multi-degree-of-freedom systems?
A: This formula is for single degree-of-freedom systems. Multi-degree systems require more complex eigenvalue analysis to determine natural frequencies.