natural frequency
Summary
Natural frequency is the frequency at which a system oscillates by itself when displaced and released. It is set by the system's own properties, such as mass, stiffness, length or tension. A driving force at this frequency produces resonance, a large-amplitude response.
Detail
Meaning: The natural frequency is the frequency at which a system oscillates when displaced and then left alone. It is set by the system's own properties, not by how hard it was disturbed. Strings and pipes have several, the fundamental and its harmonics. A periodic driving force at a natural frequency transfers energy efficiently and produces large amplitude: resonance.
Equation: Mass on a spring: f = (1/2π)√(k/m), with f in Hz, k the spring constant in N/m, m the mass in kg. Pendulum at small angles: f = (1/2π)√(g/L), with g = 9.8 m/s² and L the length in m. String fixed at both ends: fn = nv/2L, with n = 1, 2, 3…, v the wave speed in m/s.
On the MCAT: Passages ask how f changes when mass, spring constant, length or tension changes (a stiffer spring or shorter pendulum raises f; a larger mass on a spring lowers it), or whether a driving frequency produces resonance.
Common confusion: A driven system oscillates at the driving frequency, not its natural one; the natural frequency determines where the amplitude peaks. Pendulum frequency does not depend on mass, or on amplitude at small angles.
Sources
- Physics: Principles with Applications
- Fundamentals of Physics
- University Physics
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.