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III. Consider the series connections 4. Consider the series connections of the canacitors shown below: (0)...
Please help... PDE's_FOURIER SERIES Problems 1. Given the Fourier sine series cos..4.sin nls odd 0 4n...
Please help...
PDE's_FOURIER SERIES
Problems 1. Given the Fourier sine series cos..4.sin nls odd 0 4n TL n is evern m(n2-1) Determine the Fourier cosine series of sin + 2. Consider o0 sinh x ~ Σ an sin nx. Determine the coefficients an by differentiating twice.
Consider the angle shown below that has a measure of radians. Suppose that sin(0) = 0.863....
Consider the angle shown below that has a measure of radians. Suppose that sin(0) = 0.863. - - - - - - - - - a. What is the value of cos(0)? cos(O) = .5878086423 Preview * Try again. Recall that the Pythagorean Identity states that (cos(0)² + (sin(0))2 = 1 and you know the value of sin(O). Pay attention to the sign of your answer. The terminal point is to the left of the circle's center. What does that...
Consider the series RLC bandpass filter shown in (Figure 1). The filter has a quality of...
Consider the series RLC bandpass filter shown in (Figure 1). The filter has a quality of 2 and a center frequency of 8 kHz. The input to the filter is vi (t) = 23 cos wt V. Suppose that C = 5 nF. Figure < 1 of 1 + VLC с L HE + + Vi R} R V. Part E Find the voltage drop across the series combination of the inductor and capacitor when w=10w, Suppose that vlc (t)...
QUESTION 4 (4.1) Consider the variational problem with Lagrangan function 2r Sin t and endpont conditions z(0) 0, z...
QUESTION 4 (4.1) Consider the variational problem with Lagrangan function 2r Sin t and endpont conditions z(0) 0, z(*/2) = 1 (a) Find the smooth extremal of the gven vanational problem (7) (6) (b) Compare the value of the fundamental integral dt along an extremal between those two endpoints wnth the value along the curve z 1-cost through the two points Hint: You may use integration by parts and also remember that cost-(1+cos 2t), ant (1-cos 2t) and sin 2t...
5. a. Write out the first 4 partial sums of the series -(-1)". b. Is In-,(-1)"...
5. a. Write out the first 4 partial sums of the series -(-1)". b. Is In-,(-1)" a telescoping series? Explain why or why not. c. Is 29-(-1)" a conditionally convergent series? Explain why or why not. 6. Consider the series Enro esinʼn a. Explain why the integral test for determining if the series converges or diverges d not apply to this series. b. Determine whether the series converges or diverges using an appropriate test. 7. Consider the polar equation r...
exercise 4 please 1. Expand the function in a Laurent series that converges for 0 <...
exercise 4 please
1. Expand the function in a Laurent series that converges for 0 < [z] <R and determine the precise region of convergence. Show details. a. zz-1) (10%) 72-73 (10%) ez b. 2. Determine the location and order of the zeros. a. sin 2 (10%) b. coshºz (10%) 3. Residue integration a. Dedz,c: [2] = a (15%) b. $ 273dz,c: [2] => (15%) 4. Evaluate the following integrals. Show details. a. Lorem (15%) b. Lo**ay (15%)
4. Consider the amplifier shown below. The MOSFET characteristics are listed beside the circuit diagram. 12V...
4. Consider the amplifier shown below. The MOSFET characteristics are listed beside the circuit diagram. 12V MOSFET Characteristics Ks 0.5 ?nCox(W/L) K-10 A/V 2 th- VA 100 V CX) Vì 597 K 2 k a. Determine the dc operating point (ID' VDs) of MOSFETM. b. Determine the input resistance looking into the input terminals. c. Determine the output resistance looking into the output terminals. d. Determine the voltage gain Vo/V
2. LRC series circuit. [10 pts.] Consider an LRC series circuit driven by an ac voltage source Vi...
2. LRC series circuit. [10 pts.] Consider an LRC series circuit driven by an ac voltage source Vin Vo cos(wt). (a) Derive an expression for the real ac current in the circuit in terms of L, R, C, and a. (b) Determine the resonant frequency f, and angular frequency w, by direct differentiation of the current amplitude from part (a). Compare your result to LC (c) Determine the Q factor of this circuit in terms of L, R, and C....
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEM...
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEMS (c) Letting γ-IVA, reduce the equation in part (b) to the equation γ sin γ cos γ = sin (d) Use part (c) to find half of the eigenvalues explicitly and half of (e) Assuming that all the eigenvalues are nonnegative, make a list of (t)...
5. For the series RL circuit shown below with the V=10/0°, determine: a) Total impedance in...
5. For the series RL circuit shown below with the V=10/0°, determine: a) Total impedance in rectangular and phasor forms b) Find current c) Find both voltages across the resistor and capacitor d) Draw the phasor Diagram 502 3R 1002 1020° V
Please help...
PDE's_FOURIER SERIES
Problems 1. Given the Fourier sine series cos..4.sin nls odd 0 4n TL n is evern m(n2-1) Determine the Fourier cosine series of sin + 2. Consider o0 sinh x ~ Σ an sin nx. Determine the coefficients an by differentiating twice.
Consider the angle shown below that has a measure of radians. Suppose that sin(0) = 0.863. - - - - - - - - - a. What is the value of cos(0)? cos(O) = .5878086423 Preview * Try again. Recall that the Pythagorean Identity states that (cos(0)² + (sin(0))2 = 1 and you know the value of sin(O). Pay attention to the sign of your answer. The terminal point is to the left of the circle's center. What does that...
Consider the series RLC bandpass filter shown in (Figure 1). The filter has a quality of 2 and a center frequency of 8 kHz. The input to the filter is vi (t) = 23 cos wt V. Suppose that C = 5 nF. Figure < 1 of 1 + VLC с L HE + + Vi R} R V. Part E Find the voltage drop across the series combination of the inductor and capacitor when w=10w, Suppose that vlc (t)...
QUESTION 4 (4.1) Consider the variational problem with Lagrangan function 2r Sin t and endpont conditions z(0) 0, z(*/2) = 1 (a) Find the smooth extremal of the gven vanational problem (7) (6) (b) Compare the value of the fundamental integral dt along an extremal between those two endpoints wnth the value along the curve z 1-cost through the two points Hint: You may use integration by parts and also remember that cost-(1+cos 2t), ant (1-cos 2t) and sin 2t...
5. a. Write out the first 4 partial sums of the series -(-1)". b. Is In-,(-1)" a telescoping series? Explain why or why not. c. Is 29-(-1)" a conditionally convergent series? Explain why or why not. 6. Consider the series Enro esinʼn a. Explain why the integral test for determining if the series converges or diverges d not apply to this series. b. Determine whether the series converges or diverges using an appropriate test. 7. Consider the polar equation r...
exercise 4 please
1. Expand the function in a Laurent series that converges for 0 < [z] <R and determine the precise region of convergence. Show details. a. zz-1) (10%) 72-73 (10%) ez b. 2. Determine the location and order of the zeros. a. sin 2 (10%) b. coshºz (10%) 3. Residue integration a. Dedz,c: [2] = a (15%) b. $ 273dz,c: [2] => (15%) 4. Evaluate the following integrals. Show details. a. Lorem (15%) b. Lo**ay (15%)
4. Consider the amplifier shown below. The MOSFET characteristics are listed beside the circuit diagram. 12V MOSFET Characteristics Ks 0.5 ?nCox(W/L) K-10 A/V 2 th- VA 100 V CX) Vì 597 K 2 k a. Determine the dc operating point (ID' VDs) of MOSFETM. b. Determine the input resistance looking into the input terminals. c. Determine the output resistance looking into the output terminals. d. Determine the voltage gain Vo/V
2. LRC series circuit. [10 pts.] Consider an LRC series circuit driven by an ac voltage source Vin Vo cos(wt). (a) Derive an expression for the real ac current in the circuit in terms of L, R, C, and a. (b) Determine the resonant frequency f, and angular frequency w, by direct differentiation of the current amplitude from part (a). Compare your result to LC (c) Determine the Q factor of this circuit in terms of L, R, and C....
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEMS (c) Letting γ-IVA, reduce the equation in part (b) to the equation γ sin γ cos γ = sin (d) Use part (c) to find half of the eigenvalues explicitly and half of (e) Assuming that all the eigenvalues are nonnegative, make a list of (t)...
5. For the series RL circuit shown below with the V=10/0°, determine: a) Total impedance in rectangular and phasor forms b) Find current c) Find both voltages across the resistor and capacitor d) Draw the phasor Diagram 502 3R 1002 1020° V
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