LaTeX
x(t)=A\cos(\omega t+\varphi)Variables
- x(t): displacement
- A: amplitude
- ω: angular frequency
- φ: phase constant
How to use this formula
Describes ideal periodic motion whose restoring force is proportional to displacement.
Important notes
- The period is T = 2π/ω.
- Real systems may require damping and driving terms.
Quick example
With A = 2, ω = π, and φ = 0, x(1) = −2.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The period is T = 2π/ω.
- The angle unit and the domain or branch of any inverse trigonometric function must be explicit.
- Use dimensionally consistent units and the sign, coordinate, and reference-frame conventions stated for the problem.
Worked example
With A = 2, ω = π, and φ = 0, x(1) = −2.
Common mistakes
- Do not combine values with inconsistent units or sign conventions in Simple Harmonic Motion; perform a dimensional check before accepting the result.
- Verify the result of Simple Harmonic Motion with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Simple Harmonic Motion in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
x(t)=A\cos(\omega t+\varphi). - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- College Physics 2eOpenStax, Rice University — Reviewed physical quantities, units, mechanics, energy, waves, electricity, and applied formulas.
Frequently asked questions
What is the Simple Harmonic Motion used for?
Describes ideal periodic motion whose restoring force is proportional to displacement.
Can I copy this formula as LaTeX?
Yes. Copy x(t)=A\cos(\omega t+\varphi) or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.