Consider two sinusoidal currents ?2(?) = 10 cos(10??) mA ?3(?) = 10 sin(10??) mA where t...
Consider two sinusoidal currents ?2(?) = 10 cos(10??) mA ?3(?) = 10 sin(10??) mA
where t is in seconds.
-
(i) Find the total current given by ?(?) = ?2(?) + ?3(?)
-
(ii) Determine the amplitude, frequency (linear & angular), period, phase angle,
and time shift of ?(?)
Homework Answers
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Consider two sinusoidal currents ?2(?) = 10 cos(10??) mA ?3(?) =
10 sin(10??) mA
where t...
Problem 2. Consider the sinusoidal voltage given by v(t) = 25 cos(400nt + 60°) V. a....
Problem 2. Consider the sinusoidal voltage given by v(t) = 25 cos(400nt + 60°) V. a. What is the maximum amplitude of the voltage? b. What is the frequency in hertz? c. What is the frequency in radians per seconds? d. What is the phase angle in radians? e. What is the phase angle in degrees? f. What is the period in milliseconds? g. What is the first time after t=0 that v=0?
b) Let y = -6 sin(3t) – 8 cos!(Bt) be expressed in the form y =...
b) Let y = -6 sin(3t) – 8 cos!(Bt) be expressed in the form y = Rcos(wt - a), where -a sa sn. If time t is measured in seconds, determine i. The amplitude of oscillation ji. Phase angle (in radians) The angular frequency iv. The fundamental period of the resulting waveform. [9 Marks]
Given the two sinusoidal waveforms, f (t) - 10 cos (ot) 100 sin (cot), g (t)-...
Given the two sinusoidal waveforms, f (t) - 10 cos (ot) 100 sin (cot), g (t)- 40 cos (ot) - 10 sin (ot), find the phase angle by which f(t) leads g(t). (Round your answer to 2 decimal places.).
Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w,...
Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w, is a specific frequency. The system has a frequency response given by the amplitude ratio (magnitude ratio) as a function of the frequency, Mw), and the phase difference as a function of frequency, °W). Write an expression for the corresponding output in terms of the input amplitude, A1, the input frequency, W1, the amplitude ratio, and the phase difference.
Consider a sinusoidal signal?(?) = ? cos(?0? + ?). Here ?0 is the angular frequency of the signal and ? is the initial phase shift.
Consider a sinusoidal signal?(?) = ? cos(?0? + ?). Here ?0 is the angular frequency of the signal and ? is the initial phase shift.a) Draw the time domain signal. (10 Marks) b) Given that the Fourier transform pair is ? ??? ℱ ↔ 2??(? − ?), find the Fourier Transform ?(?) of ?(?). Here ?(?) is the direct delta function. (12 Marks) c) Draw the Magnitude and phase spectrums of ?(?). (8 Marks) d) Find the Fourier Transform of ?(?) = ?(?)?(?)...
Problem 1 Consider the sinusoidal signal x(t) shown below. 10 8 4 2 4 6 8...
Problem 1 Consider the sinusoidal signal x(t) shown below. 10 8 4 2 4 6 8 -10 0.2 0.4 0.6 0.8 t (seconds) (i) What is the amplitude of this signal? ii) What is the period of this signal (in seconds)? (iii) What is the frequency of this signal (in Hertz)? (iv) Write an equation for this signal.
The current from an AC source is given by: I(t) = 10.10 sin(70.0 t + 0.830...
The current from an AC source is given by: I(t) = 10.10 sin(70.0 t + 0.830 ) mA, where t is given in seconds. (a) What is the RMS current IRMS? mA (b) What is the frequency f? Hz (c) If the phase shift were given in degrees, what would its value be? degrees (d) What is the time t0 closest to t = 0 when the current vanishes? ms
The displacement of an oscillating mechanism (in m) at any time (t seconds) is given by 2.1 y-cos...
The displacement of an oscillating mechanism (in m) at any time (t seconds) is given by 2.1 y-cos(t-0.6). (a) For this situation, state (with correct unit) the following: Amplitude: Period: Frequency: Phase angle: Curve start time: (b) Draw a graph of the above function for one cycle.
The displacement of an oscillating mechanism (in m) at any time (t seconds) is given by 2.1 y-cos(t-0.6). (a) For this situation, state (with correct unit) the following: Amplitude: Period: Frequency: Phase angle:...
Consider the sinusoidal voltage v (t) = 40 cos (100t+60°) V. Part A Part D Part...
Consider the sinusoidal voltage v (t) = 40 cos (100t+60°) V. Part A Part D Part G What is the maximum amplitude of the voltage? Express your answer to three significant figures and include the appropriate units. What is the phase angle in radians? Express your answer in radians to three significant figures. What is the first time after t=0 that v=-40V? Express your answer to three significant figures and include the appropriate units. ? TO AD U veca o...
(1.2) [0.4] Express the function sin(wt + π/6) as a phase-shifted cosine. (1.3) [O.11] An SHO...
(1.2) [0.4] Express the function sin(wt + π/6) as a phase-shifted cosine. (1.3) [O.11] An SHO trajectory is given by )sin (), where t is in seconds and r is in metres. Determine the (a) equilibrium position, (b) amplitude, (c) angular frequency, (d) cycle frequency, and (e) period. (1.4) [O.14] The trajectory of an oscillating object was carefully measured and is presented on the adjacent graph. The times are in seconds, while the displacement is measured in millimetres From the...
Problem 2. Consider the sinusoidal voltage given by v(t) = 25 cos(400nt + 60°) V. a. What is the maximum amplitude of the voltage? b. What is the frequency in hertz? c. What is the frequency in radians per seconds? d. What is the phase angle in radians? e. What is the phase angle in degrees? f. What is the period in milliseconds? g. What is the first time after t=0 that v=0?
b) Let y = -6 sin(3t) – 8 cos!(Bt) be expressed in the form y = Rcos(wt - a), where -a sa sn. If time t is measured in seconds, determine i. The amplitude of oscillation ji. Phase angle (in radians) The angular frequency iv. The fundamental period of the resulting waveform. [9 Marks]
Given the two sinusoidal waveforms, f (t) - 10 cos (ot) 100 sin (cot), g (t)- 40 cos (ot) - 10 sin (ot), find the phase angle by which f(t) leads g(t). (Round your answer to 2 decimal places.).
Consider a linear, time-invariant system with an input given by X(T) = A, sin(Wit) where w, is a specific frequency. The system has a frequency response given by the amplitude ratio (magnitude ratio) as a function of the frequency, Mw), and the phase difference as a function of frequency, °W). Write an expression for the corresponding output in terms of the input amplitude, A1, the input frequency, W1, the amplitude ratio, and the phase difference.
Problem 1 Consider the sinusoidal signal x(t) shown below. 10 8 4 2 4 6 8 -10 0.2 0.4 0.6 0.8 t (seconds) (i) What is the amplitude of this signal? ii) What is the period of this signal (in seconds)? (iii) What is the frequency of this signal (in Hertz)? (iv) Write an equation for this signal.
The displacement of an oscillating mechanism (in m) at any time (t seconds) is given by 2.1 y-cos(t-0.6). (a) For this situation, state (with correct unit) the following: Amplitude: Period: Frequency: Phase angle: Curve start time: (b) Draw a graph of the above function for one cycle.
The displacement of an oscillating mechanism (in m) at any time (t seconds) is given by 2.1 y-cos(t-0.6). (a) For this situation, state (with correct unit) the following: Amplitude: Period: Frequency: Phase angle:...
Consider the sinusoidal voltage v (t) = 40 cos (100t+60°) V. Part A Part D Part G What is the maximum amplitude of the voltage? Express your answer to three significant figures and include the appropriate units. What is the phase angle in radians? Express your answer in radians to three significant figures. What is the first time after t=0 that v=-40V? Express your answer to three significant figures and include the appropriate units. ? TO AD U veca o...
(1.2) [0.4] Express the function sin(wt + π/6) as a phase-shifted cosine. (1.3) [O.11] An SHO trajectory is given by )sin (), where t is in seconds and r is in metres. Determine the (a) equilibrium position, (b) amplitude, (c) angular frequency, (d) cycle frequency, and (e) period. (1.4) [O.14] The trajectory of an oscillating object was carefully measured and is presented on the adjacent graph. The times are in seconds, while the displacement is measured in millimetres From the...
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