1. What is the Frequency of Mass Attached to Spring of Given Mass?

The frequency of a mass-spring system refers to the number of oscillations per unit time when a mass is attached to a spring. This calculation accounts for both the mass of the attached body and the mass of the spring itself, providing a more accurate frequency measurement.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( f \) — Frequency (Hz)
• \( k \) — Stiffness of Spring (N/m)
• \( M \) — Mass of Body (kg)
• \( m \) — Mass of Spring (kg)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula calculates the natural frequency of oscillation for a mass-spring system, taking into account the effective mass contribution from the spring itself (m/3).

3. Importance of Frequency Calculation

Details: Accurate frequency calculation is crucial for designing mechanical systems, understanding vibrational behavior, and ensuring structural integrity in various engineering applications.

4. Using the Calculator

Tips: Enter stiffness of spring in N/m, mass of body in kg, and mass of spring in kg. All values must be valid (stiffness > 0, masses ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: Why is the spring mass divided by 3 in the formula?
A: The m/3 term represents the effective mass contribution of the spring itself, accounting for the fact that different parts of the spring move with different amplitudes during oscillation.

Q2: What are typical frequency values for mass-spring systems?
A: Frequency values vary widely depending on the system parameters, ranging from fractions of Hz for large masses/soft springs to hundreds of Hz for small masses/stiff springs.

Q3: When is it necessary to account for spring mass?
A: Spring mass becomes significant when the mass of the spring is comparable to or greater than the attached mass. For light springs with heavy attached masses, the spring mass contribution may be negligible.

Q4: Are there limitations to this formula?
A: This formula assumes ideal spring behavior, small oscillations, and no damping. It may not be accurate for large deformations, non-linear springs, or systems with significant energy dissipation.

Q5: Can this formula be used for vertical spring systems?
A: Yes, the formula applies to both horizontal and vertical spring-mass systems, as the gravitational force affects the equilibrium position but not the oscillation frequency.