Natural frequency ω=√(k/m) sets how fast it oscillates.
A mass m on a spring k oscillates at ωₙ=√(k/m), fₙ=ωₙ/2π. Springs in parallel add stiffness; in series, 1/k=Σ1/kᵢ. Gravity only shifts the equilibrium. Static deflection δ gives ωₙ=√(g/δ).
A 2 kg mass on 800 N/m spring has fₙ≈3.2 Hz.
The natural frequency tells you how fast a system naturally oscillates, which must be kept away from excitation sources to avoid resonance.
Natural frequency ω=√(k/m) sets how fast it oscillates.
The natural frequency tells you how fast a system naturally oscillates, which must be kept away from excitation sources to avoid resonance.
Increase the stiffness or reduce the mass, because the frequency depends on the square root of stiffness over mass.
Light damping has little effect on the frequency, but it reduces the amplitude of the response over time.
Typical applications include checking that a machine foundation's natural frequency differs from its operating speed, estimating the frequency of a car body on its suspension and predicting the ringing frequency of a shelf bracket after an impact.
Study "Simple harmonic motion" first (topic 73 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Units rad/s or Hz. Effective mass of the spring adds. Stiffness from beam k=3EI/L³.
A 2 kg mass on 800 N/m spring has fₙ≈3.2 Hz.
The next topic is "Damped vibration", which builds directly on this one.
It is classed as Advanced in Engineering Mechanics (topic 74 of 106). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mechanics.
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