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The rms value for a time-dependent current I(t) is defined as I_rms = [1/T integral^T_0 I^2(t)...
In MATLAB plot the following: The function is periodic, with time period 2T=2, after t=2 the...
In MATLAB plot the following: The function is periodic, with time period 2T=2, after t=2 the same sinusoidal components repeat in the same way as when 0 st < 2. The function its expanded from one time period 27, in terms of the sinusoidal components. All sinusoidal components have frequencies which are integral multiples of the fundamental frequency. 1 1 = = = 0.5Hz to = fo = cot I am cos(womt) + b, sin(wont) m=1 rad wo = 2nfo...
1: Evaluate the following integral. Hint: (Use definition of Laplace transform. No need to integrate) i./el1-s)t...
1: Evaluate the following integral. Hint: (Use definition of Laplace transform. No need to integrate) i./el1-s)t sin(3+)dt. ii. [ -st (83 + cos(2t)dt.
all of 9 please 9. (a) If current and voltage in an ac circuit depend on...
all of 9 please
9. (a) If current and voltage in an ac circuit depend on 1(1)10 sin(2 )and V(1)-0 sin(2m), respectively, what is the time-dependent Power? P(t)-I(t)V(t) = lovo (b) From graph, what is the time-averaged value of sin (o)? (c) What is the time-averaged power? Pave . Average power IoVo (d) How are the rms values of current and voltage defined in terms of peak values? Io ms 0 rms (e) Write the time-averaged power in terms of...
1. The time-dependent Schrödinger equation The time-dependent Schrödinger equation is -R2 824(1,t) + V (1,t) (1,t)...
1. The time-dependent Schrödinger equation The time-dependent Schrödinger equation is -R2 824(1,t) + V (1,t) (1,t) = in 2m 0:2 . (a) For V1, t) = 0, show that the wave function (1,t) = A sin (kr - wt) does not satisfy the time- dependent Schrödinger equation. (b) For VI,t) = 0, Show that I, t) = A cos(kr - wt) + i sin (kr - wt) does satisfy this equation. This is a simple demonstration that the wavefunction in...
A current i(t) = 220 sin (20pi t) mA is applied to a capacitor of C...
A current i(t) = 220 sin (20pi t) mA is applied to a capacitor of C = 20000/pi mu F, as shown in the figure below: a) Knowing that i(t) = C dv/dt, integrate both sides of the equation to determine the voltage v(t). You may assume that the initial voltage is v(0) = 0.55 Volts. b) Plot one cycle of the voltage v(f) found in part a) and clearly indicate the amplitude, frequency, and period on the plot. Also,...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = ∞ e−stf(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. Find ℒ{f(t)}. (Write your
Use Definition 7.1.1.DEFINITION 7.1.1 Laplace TransformLet f be a function defined for t ≥ 0. Then the integralℒ{f(t)} = ∞e−stf(t) dt0is said to be the Laplace transform of f, provided that the integral converges.Find ℒ{f(t)}. (Write your answer as a function of s.)f(t) = et + 2ℒ{f(t)} = (s > 1)
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral L {f(t)} = estf(t) dt is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. L {f(t)} = (s > 0) f(t) (2, 2) 1 1
Select the second integral, set the start time to 0, and set the end time to...
Select the second integral, set the start time to 0, and set the end time to 3 to answer the following questions. (a) What is the value of Son f(x,y) ds for Osts 1? (b) What is the value of f(x,y) ds for 1 sts 2? (c) What is the value of f(x,y) ds for 2 st 3? (d) Using your answers from parts (a) to (c), what is the value of den f(x,y) ds + le f(x,y) ds +...
2.51 (a) The root mean-square (rms) bandwidth of a low-pass signal g(t) of finite energy is...
2.51 (a) The root mean-square (rms) bandwidth of a low-pass signal g(t) of finite energy is defined by 0O 1/2 rms where G()2 is the energy spectral density of the signal. Correspondingly, the root mean- square (rms) duration of the signal is defined by rms- &(t) dt Using these definitions, show that Assume that Ig(t)| → 0 faster than 1 / Vlt! as lt-oo (b) Consider a Gaussian pulse defined by g(t) exp(-I2) Show that, for this signal, the equality...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 2{f(t)} -6° e-str(t) dt is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. (Write your answer as a function of s.) {f(t)} = (s > 0) f(t) (2, 2) 1
In MATLAB plot the following: The function is periodic, with time period 2T=2, after t=2 the same sinusoidal components repeat in the same way as when 0 st < 2. The function its expanded from one time period 27, in terms of the sinusoidal components. All sinusoidal components have frequencies which are integral multiples of the fundamental frequency. 1 1 = = = 0.5Hz to = fo = cot I am cos(womt) + b, sin(wont) m=1 rad wo = 2nfo...
1: Evaluate the following integral. Hint: (Use definition of Laplace transform. No need to integrate) i./el1-s)t sin(3+)dt. ii. [ -st (83 + cos(2t)dt.
all of 9 please
9. (a) If current and voltage in an ac circuit depend on 1(1)10 sin(2 )and V(1)-0 sin(2m), respectively, what is the time-dependent Power? P(t)-I(t)V(t) = lovo (b) From graph, what is the time-averaged value of sin (o)? (c) What is the time-averaged power? Pave . Average power IoVo (d) How are the rms values of current and voltage defined in terms of peak values? Io ms 0 rms (e) Write the time-averaged power in terms of...
1. The time-dependent Schrödinger equation The time-dependent Schrödinger equation is -R2 824(1,t) + V (1,t) (1,t) = in 2m 0:2 . (a) For V1, t) = 0, show that the wave function (1,t) = A sin (kr - wt) does not satisfy the time- dependent Schrödinger equation. (b) For VI,t) = 0, Show that I, t) = A cos(kr - wt) + i sin (kr - wt) does satisfy this equation. This is a simple demonstration that the wavefunction in...
A current i(t) = 220 sin (20pi t) mA is applied to a capacitor of C = 20000/pi mu F, as shown in the figure below: a) Knowing that i(t) = C dv/dt, integrate both sides of the equation to determine the voltage v(t). You may assume that the initial voltage is v(0) = 0.55 Volts. b) Plot one cycle of the voltage v(f) found in part a) and clearly indicate the amplitude, frequency, and period on the plot. Also,...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral L {f(t)} = estf(t) dt is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. L {f(t)} = (s > 0) f(t) (2, 2) 1 1
Select the second integral, set the start time to 0, and set the end time to 3 to answer the following questions. (a) What is the value of Son f(x,y) ds for Osts 1? (b) What is the value of f(x,y) ds for 1 sts 2? (c) What is the value of f(x,y) ds for 2 st 3? (d) Using your answers from parts (a) to (c), what is the value of den f(x,y) ds + le f(x,y) ds +...
2.51 (a) The root mean-square (rms) bandwidth of a low-pass signal g(t) of finite energy is defined by 0O 1/2 rms where G()2 is the energy spectral density of the signal. Correspondingly, the root mean- square (rms) duration of the signal is defined by rms- &(t) dt Using these definitions, show that Assume that Ig(t)| → 0 faster than 1 / Vlt! as lt-oo (b) Consider a Gaussian pulse defined by g(t) exp(-I2) Show that, for this signal, the equality...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 2{f(t)} -6° e-str(t) dt is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. (Write your answer as a function of s.) {f(t)} = (s > 0) f(t) (2, 2) 1
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