Separate natural frequency from response amplitude
Engineering calculators (Beta)
Match the diagram conditions, then follow the example inputs and results. Change numerical values in the calculator.
1. Match the diagram to your question
ばねと減衰器でつながった物に、繰り返し力をかけるモデルです。床が揺れる式とは違います。
質量m・ばね定数k・減衰cと、加振力F₀・周波数fを入力します。
質量 m
10 kg
ばね定数 k
10 N/mm
粘性減衰係数 c
100 N·s/m
加振周波数 f
3 Hz
正弦波の力の振幅 F₀
10 N
固有振動数は系の特性、橙のXは今回の力による振幅です。共振付近は減衰の影響が大きくなります。
不減衰固有振動数 fn
5.03292 Hz
減衰比 ζ
0.158114
X · 定常応答の変位振幅 X
1.48879 mm
A spring–damper mass is driven by repeated force, rather than moving-floor excitation.
Enter mass m, spring rate k, damping c, excitation F₀ and frequency f.
Mass m
10 kg
Spring rate k
10 N/mm
Viscous damping c
100 N·s/m
Forcing frequency f
3 Hz
Sinusoidal force amplitude F₀
10 N
Natural frequency is a system property; orange X is response amplitude. Damping matters strongly near resonance.
Undamped natural frequency fn
5.03292 Hz
Damping ratio ζ
0.158114
X · Steady-state displacement amplitude X
1.48879 mm
Blue marks inputs; orange marks outputs. These diagrams explain the fixed example below; dimensions and deformation are not drawn to physical scale.
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2. Example inputs
Mass mWhat goes here?
This is mass, including fixtures or loads that move with it where required. Kilograms describe mass; newtons describe force.
10 kg
Spring rate kWhat goes here?
Spring stiffness in restoring force F=kδ.
Use the rated-range stiffness or load–deflection slope. Enter equivalent k for series/parallel combinations and distinguish preload.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
10 N/mm
Viscous damping cWhat goes here?
The coefficient in viscous force Fc=c v, not the dimensionless damping ratio ζ. They are related by c=2ζ√(km).
Required c changes with mass and stiffness and is not a universal material property. Use damper data or measured decay. These calculations apply only to the stated m and k.
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
100 N·s/m
Forcing frequency fWhat goes here?
Frequency of the applied force in cycles per second, distinct from the system’s natural frequency.
3 Hz
Sinusoidal force amplitude F₀What goes here?
Magnitude of a push or pull, in force units such as N, rather than mass in kg.
10 N
These are fixed teaching inputs. Coefficients, properties and comparison limits are not recommendations. Enter your conditions in the calculator.
3. Results for this example
Undamped natural frequency fn
5.03292 Hz
Damping ratio ζ
0.158114
Steady-state displacement amplitude X
1.48879 mm
Natural frequency is a system property; amplitude responds to the entered force and frequency. This is not a base-excitation model.
Table units are not always the units required in the formula. The calculator converts selected units to its internal base units before computing.
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Assumptions and exclusions
Linear single-degree-of-freedom spring and viscous damping, with steady sinusoidal force excitation. Base excitation, impacts, nonlinear and multi-degree-of-freedom effects are excluded. No oscillatory damped frequency is shown for ζ≥1, and no finite response amplitude is reported at undamped resonance.
