For ideal simple harmonic motion x=r cos(omega t), peak-to-peak stroke is 2r and peak acceleration magnitude is omega squared times r. At the same angular frequency, the acceleration ratio equals the amplitude ratio.
Variable Vibrating Motion Interactive Calculator
Enter two one-way harmonic amplitudes. Results compare ideal peak-to-peak stroke and same-frequency acceleration ratio—not actual acceleration, force, resonance or machine performance.
Equation Used
- Each case follows ideal one-dimensional simple harmonic motion x=r cos(omega t).
- The two cases share the same nonzero angular frequency for the acceleration-ratio comparison.
- The entered throws are one-way amplitudes and full stroke is 2r.
- Frequency, mass, force, imbalance, resonance, damping, structure, bearings, fatigue, guarding and safety are omitted.
Ideal Equal-Frequency Harmonic Comparison
NASA vibration references give x=X sin(omega t) and peak acceleration magnitude X omega squared. NASA pressure-generator work also documents a Scotch-yoke and adjustable eccentric producing simple harmonic displacement. This calculator uses only the amplitude relations below.
What This Calculator Represents
The tool doubles each entered amplitude for peak-to-peak stroke, divides the second amplitude by the first for an equal-frequency acceleration ratio and reports the signed amplitude difference.
Ideal Harmonic-amplitude Comparison
peak-to-peak stroke=2r
peak acceleration magnitude=omega squared r
for equal omega: acceleration ratio=r2/r1
signed change=r2-r1
Worked Idealized Example
For r1=1 mm and r2=6 mm, ideal peak-to-peak strokes are 2 mm and 12 mm. At the same angular frequency the peak-acceleration ratio is 6.00 and the signed amplitude change is 5 mm.
Model Boundary
- Calculated: two ideal 2r strokes, equal-frequency acceleration ratio and signed amplitude difference.
- Illustrated: two independent harmonic projection cases sharing phase.
- Not calculated: frequency, actual acceleration or g level, mass, force, imbalance, resonance, damping, structure, drive mechanism, stress, fatigue, capacity or safety.
Frequently Asked Questions
Does the calculator output actual acceleration?
No; frequency is not an input.
Why does the acceleration ratio equal the throw ratio?
Only because both cases are assumed to use the same angular frequency.
Does it calculate force?
No.
Does it predict resonance or structural response?
No.
Does it design an adjustable eccentric?
No.
Can it establish safe vibration settings?
No.
References
- NASA TP-20220018746, appendix C.2: simple harmonic displacement, velocity and acceleration, including peak acceleration X omega squared.
- NASA Tech Brief 72-10476: adjustable eccentric and Scotch-yoke produce simple harmonic piston displacement.
- NASA/CR-2006-214131: Scotch-yoke drive facility and sinusoidal piston motion.
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