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Natural Frequency Formula:
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Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force. It's a fundamental property of oscillatory systems like springs, pendulums, and electrical circuits.
The calculator uses the natural frequency formula:
Where:
Explanation: The formula shows that natural frequency increases with stiffer springs (higher k) and decreases with larger masses (higher m).
Details: Understanding natural frequency is crucial in engineering to avoid resonance (when external frequency matches natural frequency, causing large oscillations), design vibration isolation systems, and analyze structural dynamics.
Tips: Enter spring constant in N/m and mass in kg. Both values must be positive numbers. The calculator will compute the natural frequency in Hertz (Hz).
Q1: What's the difference between natural frequency and resonant frequency?
A: Natural frequency is an inherent property of the system, while resonant frequency is the frequency at which maximum oscillation occurs when an external force is applied.
Q2: How does damping affect natural frequency?
A: Damping slightly reduces the oscillation frequency to what's called the "damped natural frequency," though for lightly damped systems, the difference is negligible.
Q3: Can this formula be used for all oscillating systems?
A: This exact formula applies to simple harmonic oscillators like mass-spring systems. Other systems (pendulums, LC circuits) have similar but slightly different formulas.
Q4: What are typical natural frequency values?
A: Values vary widely - from fractions of Hz (large structures) to kHz (small mechanical components) to GHz (atomic vibrations).
Q5: How is natural frequency related to period?
A: The period (T) is the inverse of frequency: T = 1/f. Higher natural frequency means shorter oscillation period.