Versed Sine


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Related to Versed Sine: Coversed sine, coversine

versed sine

[′vərst ′sīn]
(mathematics)
The versed sine of A is 1 - cosine A. Denoted vers. Also known as versine.

Versed Sine

 

a trigonometric function. The versed sine of the angle α is equal to 1 - cos α and is written vers α. Now rarely encountered, the function was widely used until the 17th century.

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Among the differences are slight dissimilarity between the experimental and theoretical versed sine input, the suitability of the Coulomb friction to model a system with small displacement, the possibility of friction changes as the friction surface moves, and the possibility of friction differences between the two ends of the secondary beam.
Caption: FIGURE 2: Response of a single-degree-of-freedom system with friction under versed sine base input.
Caption: FIGURE 3: The maximum displacement of a single-degree-of-freedom model under versed sine base input when the level of friction is varied.
Caption: FIGURE 5: The maximum displacement response of the two masses in the friction system under a versed sine base input for different levels of friction.
Caption: FIGURE 6: Time histories and phase plane plots for the case of soft [mathematical expression not reproducible] secondary spring stiffness compared to the primary spring under a versed sine base input, mass ratio [mu] = 0.1.
Caption: FIGURE 7: Acceleration response of the primary mass of the two-degree- of-freedom model under a versed sine base input when [mathematical expression not reproducible].
Caption: FIGURE 8: The maximum displacement response of the primary mass in the friction system under a versed sine base input for different levels of friction.
Caption: FIGURE 9: Time histories and phase plane plots for the case of soft [mathematical expression not reproducible] secondary spring stiffness compared to the primary spring under a versed sine base input, mass ratio [mu] = 0.32.