forcesin

Forcesin is a term used in mathematical modeling and signal analysis to denote the sine-phase component of a time-varying force within a dynamic system. While not a standard designation in established physics texts, it appears in some teaching materials and software documentation to describe the extraction of a force signal’s sine component at a specified frequency.

Definition and relation to Fourier analysis

For a periodic force F(t) with period T = 2π/ω, the forcesin at frequency ω can be defined as F_sin(ω) = (2/T) ∫_0^T F(t) sin(ω t) dt. If F(t) has a Fourier series F(t) = a0/2 + Σ[a_n cos(nω0 t) + b_n sin(nω0 t)], then forcesin at ω = nω0 corresponds to the sine coefficient b_n. For non-periodic signals, an equivalent coefficient can be obtained over a chosen time window or via a discrete sine transform, applying the same principle of projecting the force onto a sine basis at the target frequency.

Applications

Forcesin is used conceptually to analyze vibration and dynamic response, enabling separation of the sine-phase component of a force from other harmonic or noise contributions. It is helpful in signal processing, modal analysis, and control design where understanding the sine-demand at specific frequencies aids in assessing damping, resonance, or phase relationships.

Computational notes and limitations

In practice, forcesin can be computed with numerical methods, such as the discrete sine transform or windowed integrals. The approach depends on the chosen frequency and window length. Limitations include sensitivity to windowing, non-stationarity of the signal, and the fact that it captures only the sine component at a single frequency, not a full spectrum.

See also

Fourier coefficient, sine component, discrete sine transform, harmonic analysis, modal analysis.