Mihir Raj RathoreMechanical engineer · M.Eng.

Technical notes / Vibration playground

Schematic / illustrativeGenerated signals, not measured data

Vibration playground

A single mass on a spring and damper. Change mass, stiffness and damping, tap it or drive it, and watch the signal, its spectrum and the five features from my thesis work.

Parameters

The natural frequency is fn = √(k/m) / 2π. Drive the system near fn to see resonance.

–Natural freq.
–RMS
–Crest factor
–Excess kurtosis
Displacement vs time–
Spectrum (FFT, 0–60 Hz)dashed: natural frequency
Mass on spring and damper (scaled)t = 0.00 s

Things to try

Set a sine drive near the natural frequency and the amplitude grows. Raise the damping ratio and the resonance peak flattens and the free ring-down after a tap dies out faster. Tap the system with low damping and the crest factor and kurtosis rise, because the signal is dominated by a short, decaying burst. Add noise to see how it hides small peaks in the spectrum.

Method: the equation of motion m·x″ + c·x′ + k·x = F(t) is integrated numerically at 1 kHz for 2.048 s. The spectrum is a Hann-windowed FFT. RMS, crest factor and excess kurtosis are computed on the displacement signal after removing the mean. Everything is generated in your browser and none of it is measured data. Read the note on vibration features for what each number means.