Pj Problems - Overview
The Number Line
7 Spaces Of Interest - Overview
Triadic Unit Mesh
States Of Matter
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Faith, Love, Charity
Signaling is a ubiquitious phenomenon in the societies of cognitive beings.
(a) What is a signal?
(b) What is a periodic signal?
(c) Identify the following periodic waveforms:
S7P1A17 (Containership -Location)
S7P2A21 (Identity - Physical Properties).
Pj Problem of interest is of type identity.
(a) Signals are essentially indicators of presence (the being in a location). Thereafter, one is interested in the identity, analyses and possible uses of the presence. In electric circuits, the voltage and current signals indicate the presence of voltage and current sources. The identities of voltage and current signals are expressed as waveforms (graphical representations of functions).
(b) Periodic Signals are time-dependent cyclic signals. In other words, there is an interval called the period of the signal during which the signal repeats the same waveform pattern.
Mathematically, an arbitrary signal x(t) is periodic if it can be expressed as follows:
x(t) = x(t + nT)-------(1)
Where n = 1, 2, 3 ...; and T is the period (the time it takes to complete 1 cycle) of x(t).
The frequency (f) of x(t) in cycles/sec (Hertz) is:
f = 1/T-------(2)
(ci) The waveforms in c(i) are cosine and sine periodic signals (sinusoids).
The red waveform is a cosine function. Its general form is:
v(t) = Vmaxcosω----(3)
Where the radian frequency (angular velocity), ω = 2πf.
The signal expressed in (3) is often the reference sinusoid.
A sinusiodal signal has the general form:
v(t) = Vmaxcos(ωt + θ)-----(4)
The sinusiodal signal expressed in equation (4) is said to lead the sinusiodal signal expressed in equation (3) by phase angle, θ.
The phase angle θ = ωτ
Where τ is the time shift
The Blue waveform is a sine function. Its general form is:
v(t) = Vmaxsinωt----(5)
The relationship between the cosine signal and the sine signal is:
Vmaxcosωt = Vmaxsin(ωt + π/2)----(6).
Since the cosine signal leads the sine signal by π/2.
The relationship can also be expressed as follows:
Vmaxsinωt = Vmaxcos(ωt - π/2)----(7).
Since the sine signal lags the cosine signal by π/2.
(cii) The waveforms in c(ii) is a periodic pulse signal.
(ciii) The waveform in c(iii) is a periodic sawtooth signal.
The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle
Derivation Of The Area Of An Ellipse
Derivation Of Volume Of A Cylinder
Derivation Of Volume Of A Sphere
Derivation Of Volume Of A Cone
Derivation Of Volume Of A Torus
Derivation Of Volume Of A Paraboloid
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Ordinary Differential Equations (ODEs)
Infinite Sequences And Series
Introduction To Group Theory
Advanced Calculus - Partial Derivatives
Advanced Calculus - General Charateristics Of Partial Differential Equations
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Derivation Of Heat Equation For A One-Dimensional Heat Flow
The Universe is composed of matter and radiant energy. Matter is any kind of mass-energy that moves with velocities less than the velocity of light. Radiant energy is any kind of mass-energy that moves with the velocity of light.
Composition And Structure Of Matter
How Matter Gets Composed
How Matter Gets Composed (2)
Molecular Structure Of Matter
Molecular Shapes: Bond Length, Bond Angle
Molecular Shapes: Valence Shell Electron Pair Repulsion
Molecular Shapes: Orbital Hybridization
Molecular Shapes: Sigma Bonds Pi Bonds
Molecular Shapes: Non ABn Molecules
Molecular Orbital Theory
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