Natural frequency

Definition

Natural frequency is the frequency at which a system oscillates when not subjected to a continuous or repeated external force. It is determined by the system's physical properties such as mass and stiffness.

5 Must Know Facts For Your Next Test

1. Every oscillatory system has its own natural frequency, which depends on its physical characteristics.
2. When an external force matches the natural frequency, resonance occurs, leading to a significant increase in amplitude.
3. In mechanical systems, natural frequency can be calculated using $f_0 = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$, where $k$ is the stiffness and $m$ is the mass.
4. Electrical systems also have natural frequencies determined by inductance and capacitance, given by $f_0 = \frac{1}{2\pi} \sqrt{\frac{1}{LC}}$.
5. Identifying and controlling natural frequencies is crucial in engineering to avoid destructive resonant conditions.

Review Questions

• What happens when an external force matches a system's natural frequency?
• How do you calculate the natural frequency of a mechanical oscillator?
• Why is it important to identify and control natural frequencies in engineering?

Related terms

Resonance:

The phenomenon that occurs when a system is driven at its natural frequency, leading to maximum energy transfer and large amplitude oscillations.

Damping:

A process or mechanism that reduces the amplitude of oscillations over time through energy dissipation.

Forced Oscillation: Oscillations that occur when an external periodic force acts on a system.