What is the phase relationship and amplitudes between the F(t) and G(t) functions?
F(t) = -ieiωt and G(t) = [1+i*sqrt(3)]*eiωt
F(t) = (3 - 4i)*eiωt and G(t) = (-3 + 4i)*eiωt
What is the phase relationship and amplitudes between the F(t) and G(t) functions? F(t) = -ieiωt...
Aeroacoustics
What is the phase relationship between: a) F(t) = eiat and G(t)-ei(at-π/2) b) F(t)-ieo and G(t) c) F(t)--ieior and G(i)=(1+W3)eiat d) F(t)-(3-4)eat and G(t)=(-3+4i)eiat e) F(t)--i(i + V3)ei(or+ π /6) and G(t)--dat 3. iot
What is the phase relationship between the voltage v(t) = 65 sin(or - 45') and current i(t) = 20 sin( +90°)? i(t) lags v(t) by 0 = (note: 0 is a positive or negative angle in degrees)
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to E I, then f and g are linearly independent for all te I. • If f(t) and g(t) are linearly dependent on I, then W (8,9)(t) = 0 for allt € 1. Note: This does NOT say that "If W(8,9)(x) = 0, then f(x) and g(2) are linearly dependent. Problem 2 Determine if the following functions are...
QUESTION 2 Given two periodic functions, f(t) and g(t) is defined by and f (t) = cos, -<t<t f(t)= f(t +26) g(t) = cos, 0<t<2n g(t) = g(t +21) Sketch the graph of the periodic functions f(t) and g(t) over the interval (-37,37). Sketch in separate graphs. (Please use any online graphing software not hand-drawn). Find the Fourier series of f(t) and g(t). (b) Then, briefly comment what do you observe from the graphs and the Fourier series expansion of...
(a) Show that the functions f(t) = t2t1 and g(t) = t3 are linearly dependent on 0 < t < 1 and on -1<t< 0 (b) Show that f(t) and g(t) are linearly independent on -1 <t<1. (c) Show that W(f,g)(t) is zero for all -1<t<1.
4.) Find the amplitudes of each of the following harmonic synchronous oscillations and the phase angle between the oscillations. (20 pts) xi(t) = 3cos(20t) - 4sin(20) x:(t)= 1.5sin(20t - 1/6) - 2cos(20t) 5.) Represent the two harmonics from problem #4 in the time domain, frequency domain, using phasors and complex numbers. (20 pts) 6.) Calculate the amplitude and the phase of the oscillation that results from the composition of the two harmonic synchronous oscillations in problem #4. (10 pts)
(1 point) The functions f(t) and g(t) are shown below. 11.0 f(t) g(t) If the motion of a particle whose position at time t is given by z = f(t), y = g(t), sketch a graph of the resulting motion and use your graph to answer the following questions: (a) The slope of the graph at (0.25, 0.5) is 6 (enter undef if the slope is not defined) (b) At this point the particle is moving to the right and...
*9. For each of the following pairs of functions, determine the highest order of contact between the two functions at the indicated point xo: (e) f,g : R-R given by f(x)and g(x) 1+2r ro0 (f) f, g : (0, oo) → R given by f(r) = In(2) and g(z) = (z-1)3 + In(z): zo = 1. (g) f.g: (0, oo) -R given by f(x)-In(x) and g(x)-(x 1)200 +ln(x); ro 1 x-1)200
*9. For each of the following pairs of functions,...
Problem #7; Consider the functions f(t = e' and g(f) = e 3 defined on 0 t < co. (a) (f*g)(t) can be calculated as h(w, tdw Enter the function h(w, t into the answer box below Hs)}. Enter the function H(s) into the answer box below (b) (f* g)(t) can also be calculated as L (c) Evaluate (f* g)(t) Enter your answer as a symbolic function of w,t, as in these examples Problem #7(a): Enter your answer as a...
4. Find the convolution of the following functions a. f(t)=t g(t) = sin 3t b. f(t)=é g(t)=cos2t