// multi-utility computation suite · offline · instant · precise
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eng.beam-forced-vibration Calculator
Calculates steady-state amplitude and dynamic magnification factor for a forced-vibration system near resonance. The dynamic magnification factor reaches 1/(2ζ) at resonance — a lightly damped system (ζ = 0.01) amplifies the static deflection by 50× at resonance.
Inputs
F0 N
Maximum displacement from equilibrium. Energy carried by a wave is proportional to amplitude squared.
K N M
Reference formula or conversion factor shown for context.
Fn Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
F Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Zeta
Reference formula or conversion factor shown for context.
Results
static deflection X_st (mm)
Maximum lateral displacement of the beam under load. Codes typically limit to L/360 for floors (to avoid cracking finishes) or L/240 for roofs. Excessive deflection signals the beam is undersized.
dynamic magnification factor DMF
A dimensionless multiplier applied in the calculation.
amplitude X (mm)
Reference formula or conversion factor shown for context.
phase lag φ (°)
The current phase of the cycle or process.
DMF = 1/√((1-r²)²+(2ζr)²)
Reference formula or conversion factor shown for context.