Model forced vibration response with structured inputs. Compare damping effects near resonance and operating speed. Export results, review formulas, and validate design assumptions fast.
Sample case: natural frequency = 12 Hz, damping ratio = 0.08, static deflection = 1.50 mm.
| Excitation Frequency (Hz) | Natural Frequency (Hz) | Damping Ratio | Frequency Ratio | Magnification Factor | Dynamic Displacement (mm) |
|---|---|---|---|---|---|
| 6.00 | 12.00 | 0.08 | 0.5000 | 1.3258 | 1.9887 |
| 10.00 | 12.00 | 0.08 | 0.8333 | 2.9996 | 4.4994 |
| 12.00 | 12.00 | 0.08 | 1.0000 | 6.2500 | 9.3750 |
| 15.00 | 12.00 | 0.08 | 1.2500 | 1.6750 | 2.5126 |
| 18.00 | 12.00 | 0.08 | 1.5000 | 0.7856 | 1.1785 |
The calculator uses standard forced vibration relations for a damped single degree of freedom system.
Use consistent units. Frequencies are in hertz. Mass is in kilograms. Stiffness is in newtons per meter. Static and dynamic displacement are shown in millimeters.
The magnification factor shows how much a vibrating system amplifies motion under harmonic forcing. It is a key measure in engineering design. It helps estimate displacement growth, resonance risk, and damping effects during real operating conditions.
The main driver is the frequency ratio. This ratio compares excitation frequency with natural frequency. When the ratio approaches one, the system moves toward resonance. Response can increase sharply. Even a modest forcing load may then create large motion.
Damping limits how strongly vibration grows near resonance. Low damping creates a taller response peak. Higher damping spreads the response and reduces the maximum value. This matters for rotating equipment, machine frames, supports, and spring mounted systems.
Engineers use magnification factor calculations for fans, pumps, motors, blowers, test rigs, and other forced vibration problems. The value helps compare operating speed with the system natural frequency. It also supports early design screening before deeper simulation or testing.
In practice, not every parameter is known directly. Sometimes natural frequency comes from mass and stiffness. Sometimes damping ratio comes from damping coefficient data. Static deflection may also come from force and stiffness. This calculator handles those linked inputs to speed up engineering work.
If the operating point sits close to resonance, motion can rise fast. That can increase stress, noise, looseness, and fatigue. Engineers often respond by changing stiffness, mass, damping, or operating speed. Reviewing magnification factor early supports safer and more reliable design choices.
The result table reports frequency ratio, magnification factor, phase angle, and dynamic displacement. Together, these values describe how the system reacts to forcing. They also show whether the machine is below resonance, near resonance, or above resonance.
It is the ratio between dynamic response and static response for a forced vibration system. It shows how much motion is amplified by excitation at a given frequency and damping level.
When excitation frequency approaches natural frequency, the system stores and transfers energy more efficiently. That increases response amplitude. Low damping makes this peak much higher.
Yes, for this common forced vibration model, higher damping reduces the resonance peak and limits displacement growth. It improves control of motion near the critical region.
Yes. If you provide mass and stiffness, the calculator derives natural frequency automatically. That helps when design data is available but the frequency was not precomputed.
Phase angle shows how far the response lags the applied force. It is useful for understanding motion timing, dynamic behavior, and resonance transition in rotating or oscillating systems.
Use hertz for frequency, kilograms for mass, newtons per meter for stiffness, and newton second per meter for damping coefficient. Static deflection is entered in millimeters.
Yes. If static deflection is entered or derived, the page multiplies it by the magnification factor. That gives the dynamic displacement in millimeters.
No. It is a strong screening and educational tool. Final design should also consider full loading, boundary conditions, material limits, testing, and detailed dynamic analysis.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.