1. What is Natural Frequency?

Natural frequency is the frequency at which a system oscillates when not subjected to a continuous or external force. It's a fundamental property of mechanical systems described by the formula:

2. How Does the Calculator Work?

The calculator uses the natural frequency equation:

Where:

• \( f \) — Natural frequency (Hz)
• \( k \) — Spring constant (N/m)
• \( m \) — Mass (kg)
• \( \pi \) — Mathematical constant Pi (~3.14159)

Explanation: The equation shows that natural frequency increases with higher spring stiffness and decreases with larger mass.

3. Importance of Natural Frequency

Details: Understanding natural frequency is crucial for avoiding resonance in mechanical systems, designing structures, and analyzing vibrations in engineering applications.

4. Using the Calculator

Tips: Enter spring constant in N/m and mass in kg. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What happens at natural frequency?
A: When a system is excited at its natural frequency, resonance occurs, leading to large amplitude oscillations that can cause structural damage.

Q2: How is this different from forced frequency?
A: Natural frequency is intrinsic to the system, while forced frequency is imposed by external periodic forces.

Q3: What are typical natural frequency values?
A: Values vary widely - from fractions of Hz for large structures to kHz for small mechanical components.

Q4: Does damping affect natural frequency?
A: Yes, damping slightly reduces the actual oscillation frequency from the theoretical natural frequency.

Q5: Can this be used for all vibration systems?
A: This formula applies to simple harmonic oscillators. More complex systems require advanced analysis.