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Problem 3 (4 points) NEAR-RESONANCE CASE. (1) Determine the frequency and period of the beats, (2...
1. Oscillating system performs damped oscillations with frequency 1000 Hz. Determine the frequency of natural oscillations...
1. Oscillating system performs damped oscillations with frequency 1000 Hz. Determine the frequency of natural oscillations if the resonance frequency is 998 Hz. 2. Amplitude of vibrations during 5 minutes decreased by 2 times, during which time the amplitude reduced by 8 times? 3. For 8 minutes amplitude decreased 8 times. Find damping factor. 4. Determine how much resonance frequency is different from the natural oscillation frequency (1kHz) when the damping factor is 400 s decreased 20 times 6. The...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral s...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution. ar dY (1 -3 dt Y,
Problem 3. For the...
1. find the frequency-domain impedance, Z, as shown in the figure below. 2. Determine the period...
1. find the frequency-domain impedance, Z, as shown in
the figure below.
2. Determine the period of current in ms.
Z 862 322 Given ilt): 3 cos (3901 - 130°) A
2.4.1. Suppose (t is as shown 3-2 1 3 4 (a) Determine the fundamental period To,...
2.4.1. Suppose (t is as shown 3-2 1 3 4 (a) Determine the fundamental period To, the fundamental frequency fo, and the funda- mental cycle x(t). Express a(t) as a function involving a rect(.) (b) Determine X(f), the Fourier transform of the fundamental cycle a(t) (c) Determine the Fourier series coefficients xk for ï(t) (d) DetermiX(f), the Fourier transform of (t) (e) Determine the power P (f) Determine the percentage of power in DC and the percentage of power in...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fund...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2...
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2 cos(7t 2) Determine also the signal's fundamental radian frequency w. No integration is required to solve this problem.
3.(2 points) Determine whether the given function is periodic. If so, find its funda- mental period....
3.(2 points) Determine whether the given function is periodic. If so, find its funda- mental period. (a) f(x) = 24 (b) f(x) = sin(ſx) (c) f(x) = ln x + cos x (d) f(x) = cos(65 4.(3 points) Sketch the graph of the given function defined on an interval (-0, 0) if (a) f(x) = e" for x > 0 and f(x) is an even function. (b) f(x) = {x, 0 < x < 2 (b) [(*) = 10, x=2...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are i...
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
4. (20 points) A current waveform shown in the Fig. 4. | (mA) t(s) -3 -2...
4. (20 points) A current waveform shown in the Fig. 4. | (mA) t(s) -3 -2 -1 1 2 3 4 5 6 Figure 4: Current waveform flowing through an inductor. (a) (15 points) Determine the capacitor voltage at t=1s, 3s, and 5s, which results from the capacitor with capacitance C = 311F. Capacitor voltage was 3V at -1s. (b) (5 points) Sketch the capacitor voltage.
1. Oscillating system performs damped oscillations with frequency 1000 Hz. Determine the frequency of natural oscillations if the resonance frequency is 998 Hz. 2. Amplitude of vibrations during 5 minutes decreased by 2 times, during which time the amplitude reduced by 8 times? 3. For 8 minutes amplitude decreased 8 times. Find damping factor. 4. Determine how much resonance frequency is different from the natural oscillation frequency (1kHz) when the damping factor is 400 s decreased 20 times 6. The...
Problem 3. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution. ar dY (1 -3 dt Y,
Problem 3. For the...
1. find the frequency-domain impedance, Z, as shown in
the figure below.
2. Determine the period of current in ms.
Z 862 322 Given ilt): 3 cos (3901 - 130°) A
2.4.1. Suppose (t is as shown 3-2 1 3 4 (a) Determine the fundamental period To, the fundamental frequency fo, and the funda- mental cycle x(t). Express a(t) as a function involving a rect(.) (b) Determine X(f), the Fourier transform of the fundamental cycle a(t) (c) Determine the Fourier series coefficients xk for ï(t) (d) DetermiX(f), the Fourier transform of (t) (e) Determine the power P (f) Determine the percentage of power in DC and the percentage of power in...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2 cos(7t 2) Determine also the signal's fundamental radian frequency w. No integration is required to solve this problem.
3.(2 points) Determine whether the given function is periodic. If so, find its funda- mental period. (a) f(x) = 24 (b) f(x) = sin(ſx) (c) f(x) = ln x + cos x (d) f(x) = cos(65 4.(3 points) Sketch the graph of the given function defined on an interval (-0, 0) if (a) f(x) = e" for x > 0 and f(x) is an even function. (b) f(x) = {x, 0 < x < 2 (b) [(*) = 10, x=2...
4. (20 points) Consider the periodic signal r(t) shown in the Figure below: x(t) 3 2 N VAA 0 1 2 3 4 5 6 A . Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
4. (20 points) A current waveform shown in the Fig. 4. | (mA) t(s) -3 -2 -1 1 2 3 4 5 6 Figure 4: Current waveform flowing through an inductor. (a) (15 points) Determine the capacitor voltage at t=1s, 3s, and 5s, which results from the capacitor with capacitance C = 311F. Capacitor voltage was 3V at -1s. (b) (5 points) Sketch the capacitor voltage.
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