The function determines the exact shape of the wave f.Similarly, the wave travelling along the negative direction of the x-axis could be y=f(t+xv); hence, the function y=f(t±xv) represents progressive waves along the x-axis.Some Terms Related to Progressive Waves...
Equation (2) is referred to as a wave equation since its solutions consist of sinusoidal traveling waves with amplitude E. These waves consist of oscillating electric and magnetic fields, and are thus known as EM waves. The optical properties of any material can be understood in terms of the...
The solution to this equation is sinusoidal, whereAis the amplitude of oscillation (the farthest the mass gets from equilibrium), is the angular frequency of oscillation, andϕis the phase, which captures the initial position and velocity of the mass at timet= 0. The period is related to ...
Then Re[] implies taking the real part of the quantity in brackets, and ω is the angular frequency of the sinusoidal excitation. In addition, using the phasor representation, computing the derivatives with respect to time results in (2.2)∂∂t[F→s(r→)ejωt]=jωF→s(r→)ejωt...
A circle can be described by an equation that results from the application of theformula for adrawn in the circle. This triangle will have the hypothenuse equal to the radius of the circle, and the other sides given by segments over the x and y-axis. Substituting these elements in the ...
The effect of the modulator is modeled through its transmission function, written as e−m(t), where m(t) represents the modulator state. Our analysis is valid for any periodic function of time m(t), but here we will focus on the classic sinusoidal case m(t)=M[1−cos(ΩMt)]...
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Considering the sinusoidal waveform, the phase difference is explained as the time gap where the wave either falls behind or leads in correspondence to another wave. This term is just a characteristic of a single wave and it is the relative characteristic of either two or more waves. This is...
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,yn (or the determinant of Wronski).Theorem 12.1 Let (12.2)y(n)+a1(x)y(n−1)+⋯+an−1(x)y′+an(x)y=0 be the homogeneous linear equation of order n with a1,a2,…,an continuous functions on interval I⊂R. Let y1,y2,…,yn be the solutions of the given equation on ...