Controlled engineering arithmetic
Single-Frequency Sinusoidal Vibration Quantity Conversion Worksheet
Convert displacement, velocity and acceleration magnitudes only after declaring the frequency, units and RMS/peak convention. An optional velocity-level result uses your controlled RMS reference. This is not broadband conversion, condition assessment or ISO compliance.
Converted magnitudes
No current numerical result is available.
Formula and dimensional boundary
For x(t) = Xpk sin(ωt), with ω = 2πf:
Dimensions: X is length [L], V is [L T⁻¹], A is [L T⁻²], f is [T⁻¹], and ω is rad/s (the radian is dimensionless in SI dimensional analysis). The equations are general calculus for one sine, not formulas issued by ISO 1683, ISO 2041 or ISO 20816.
Source register and permitted use
| ไอดี | Controlled source and lifecycle | Used for | Not used for |
|---|---|---|---|
| S1 | NASA NTRS N76-26818, Chapter 9, p. 383 — public full text | Single-sine amplitude equations and RMS/peak relation. | No broadband, severity or ISO claim. |
| S2 | JCGM 200:2012 VIM3, 2.12 | Conventional gn = 9.80665 m/s². | Not local gravity or a limit. |
| S3 | NIST SI Units — Length | Exact 1 in = 25.4 mm; 1 mil = 25.4 μm. | No rounded 0.03937 factor or severity. |
| S4 | BIPM SI Brochure, 9th edition, updated 2026 | Current SI unit/symbol framing. | No vibration criteria. |
| S5 | ISO 1683:2015, Edition 3 — confirmed 2025, current | Lifecycle and public scope of preferred reference values. | Exact protected values/applications: NEEDS_LICENSED_SOURCE; none embedded. |
| S6 | ISO 2041:2018, Edition 4 — confirmed 2024, current | Lifecycle and vocabulary scope. | Protected definitions: NEEDS_LICENSED_SOURCE; no clause invented. |
| S7 | ISO 20816-1:2016, Edition 1 — published, to be revised | Public caution to define quantity/method/limitations. | No universal severity table or conversion verdict. |
| S8 | ISO 10816-1:1995 + Amd 1:2009 — withdrawn | Historical lifecycle only. | Not current authority. |
Corrections made during review
The embedded ISO dB reference was removed
The public ISO card does not expose the protected exact values/application distinctions. A level now requires the user’s positive RMS reference and controlled basis.
Broadband use is now gated
The derivative relationships are exact for a sine. An overall broadband RMS value cannot be converted at one frequency without a spectrum/model.
Exact inch factors replaced rounded factors
International inch conversion uses exactly 0.0254 m, and one mil is exactly 25.4 μm.
Zero amplitude is explicit
Linear quantities remain zero; a requested logarithmic ratio is −∞ dB rather than NaN, Infinity text or a hidden dash.
RMS/peak meaning is traceable
The input convention is required, the sine assumption is an evidence gate and every output label states its convention.
Persistence and detached export were removed
No defaults, presets, auto-calculate, URL state, browser storage, clipboard or dynamic result HTML remains.
Obsolete ISO 10816 framing was removed
ISO 10816-1 is recorded as withdrawn; this page never labels a converted magnitude as an ISO condition result.
External runtime dependencies were removed
Formulas use readable native markup; no external fonts, KaTeX or CDN is required.
