1. What is Natural Frequency?

Natural frequency is the frequency at which a system oscillates when not subjected to a continuous or external force. For a mass-spring system, it depends on the spring constant and the mass.

2. How Does the Calculator Work?

The calculator uses the natural frequency formula:

Where:

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

Explanation: The formula shows that frequency increases with stiffer springs (higher k) and decreases with larger masses.

3. Importance of Natural Frequency

Details: Understanding natural frequency is crucial for designing mechanical systems, avoiding resonance in structures, and analyzing vibrational behavior 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: Systems tend to oscillate with maximum amplitude when excited at their natural frequency, a phenomenon called resonance.

Q2: How does damping affect natural frequency?
A: Damping slightly reduces the oscillation frequency, though this calculator assumes an undamped system.

Q3: Can this be used for pendulum systems?
A: No, pendulums have a different natural frequency formula that depends on length and gravity.

Q4: What are typical natural frequency ranges?
A: Varies widely - from fractions of Hz (large structures) to kHz (small mechanical components).

Q5: How does this relate to angular frequency?
A: Angular frequency (ω) is related by ω = 2πf, and can be directly calculated as √(k/m).