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  2. Brachistochrone curve - Wikipedia

    en.wikipedia.org/wiki/Brachistochrone_curve

    The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...

  3. Slope - Wikipedia

    en.wikipedia.org/wiki/Slope

    Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

  4. Motion graphs and derivatives - Wikipedia

    en.wikipedia.org/wiki/Motion_graphs_and_derivatives

    The green line shows the slope of the velocity-time graph at the particular point where the two lines touch. Its slope is the acceleration at that point. Its slope is the acceleration at that point. In mechanics , the derivative of the position vs. time graph of an object is equal to the velocity of the object.

  5. Shock response spectrum - Wikipedia

    en.wikipedia.org/wiki/Shock_response_spectrum

    Calculate (by direct time-domain simulation) the maximum instantaneous absolute acceleration experienced by the mass element of your SDOF at any time during (or after) exposure to the shock in question. This acceleration is a; Draw a dot at (f,a); Repeat steps 2–4 for many other values of f, and connect all the dots together into a smooth curve.

  6. Radius of curvature - Wikipedia

    en.wikipedia.org/wiki/Radius_of_curvature

    For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof. [1] [2] [3]

  7. Archimedean spiral - Wikipedia

    en.wikipedia.org/wiki/Archimedean_spiral

    Scroll compressors, used for compressing gases, have rotors that can be made from two interleaved Archimedean spirals, involutes of a circle of the same size that almost resemble Archimedean spirals, [4] or hybrid curves. Archimedean spirals can be found in spiral antenna, which can be operated over a wide range of frequencies.

  8. Semi-log plot - Wikipedia

    en.wikipedia.org/wiki/Semi-log_plot

    In other words, F is proportional to the logarithm of x times the slope of the straight line of its lin–log graph, plus a constant. Specifically, a straight line on a lin–log plot containing points ( F 0 , x 0 ) and ( F 1 , x 1 ) will have the function:

  9. Centripetal force - Wikipedia

    en.wikipedia.org/wiki/Centripetal_force

    A centripetal force (from Latin centrum, "center" and petere, "to seek" [1]) is a force that makes a body follow a curved path.The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.