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Tay, Mareels and Moore (1998) defined settling time as "the time required for the response curve to reach and stay within a range of certain percentage (usually 5% or 2%) of the final value." [ 2 ] Mathematical detail
A Magic Triangle image mnemonic - when the terms of Ohm's law are arranged in this configuration, covering the unknown gives the formula in terms of the remaining parameters. It can be adapted to similar equations e.g. F = ma, v = fλ, E = mcΔT, V = π r 2 h and τ = rF sinθ.
Symbol Name Meaning SI unit of measure alpha: alpha particle: angular acceleration: radian per second squared (rad/s 2) fine-structure constant: unitless beta: velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian
The settling time is the time for departures from final value to sink below some specified level, say 10% of final value. The dependence of settling time upon μ is not obvious, and the approximation of a two-pole system probably is not accurate enough to make any real-world conclusions about feedback dependence of settling time.
basic physics formula triangles: Image title: Image mnemonics in the style of the Ohm's law formula triangle for high-school physics by CMG Lee. Covering the unknown in each mnemonic gives the formula in terms of the remaining parameters. In the SVG file, hover over a symbol for its meaning and formula. Width: 100%: Height: 100%
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
Illustration of the effect of varying the Stokes number. Orange and green trajectories are for small and large Stokes numbers, respectively. Orange curve is trajectory of particle with Stokes number less than one that follows the streamlines (blue), while green curve is for a Stokes number greater than one, and so the particle does not follow the streamlines.
In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. [1] These values may be expressed as ratios [ 2 ] or, equivalently, as percentages [ 3 ] with respect to a given reference value.