Homework Answers
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Differential equation
For a 2^nd order DE Lq + Rq + (1/C)q = 0 a) Show...
Solve the initial value problem honhomogeneous equation: LQ"+RQ+ Q = E. coswt initial Conditions: SQ (0)=Qe,...
Solve the initial value problem honhomogeneous equation: LQ"+RQ+ Q = E. coswt initial Conditions: SQ (0)=Qe, Q (0) = Q! as follows: + First solve the associated homogeneous lequation LQ"+RQ'TEQ =0 by using the characteristic equation Irt art &r=0 to obtain three types of solutions 2 Next show how to find a particular solution Qp to the non homogeneous equation by showing Oplt) = t-Lw²coswt twR sin (wt) ( - Lw²) 4 w²R Eo Show in detail that you can...
3. Show that the differential equation 1 d de sin sin 0 de de sin20 Lastl...
3. Show that the differential equation 1 d de sin sin 0 de de sin20 Lastl leads to the associated Legendre equation if we consider the c= cos0, A- v(v+1), ux)-e(0)
(a) For the circuit of Figure 4, assuming a sinusoidal is(t) (0) Prove that the resonant frequeney is given by o- (3 marks) LC (ii) If the total admittance at resonance is 20 ms (seen by the source)...
(a) For the circuit of Figure 4, assuming a sinusoidal is(t) (0) Prove that the resonant frequeney is given by o- (3 marks) LC (ii) If the total admittance at resonance is 20 ms (seen by the source) with resonant frequency of wo 5000 rad/s and quality factor of Q-10, calculate the values of R L, C, the bandwidth and half-power frequencies in Hertz. (4 marks) VG and hence show (iii) Derive an expression for the driving point impedance Z(jø)...
Problem 2. (1 point) If the differential equation de + 3x = 0 is overdamped, the...
Problem 2. (1 point) If the differential equation de + 3x = 0 is overdamped, the range of values for mis? Your answer will be an interval of numbers given in the form (1.2) 11.2).(-6), etc.
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the s...
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
(2 points) Two driven inductors A R = 1 kΩ resistor, a L1 = 20 mH...
(2 points) Two driven inductors A R = 1 kΩ resistor, a L1 = 20 mH inductor and a L2 28 mH inductor are connected in series. A funtion generator drives the circuit with a 5 Vpp variable frequency sine wave. (a) What is the equivalent impedance Zeq of this circuit? O A. R +jwLIL2/(L1+ L2) E. None of these (b) For what angular frequency does |Zoq v2 R? 20833.3 radians/sec (c) What is the peak-to-peak value of the voltage...
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determi...
#2 ONLY PLEASE
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*)...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
Rs 100Ω resistor C- 10 uF capacitor L- 120 mH inductor Write the impedance Z [Q] equation for the...
Rs 100Ω resistor C- 10 uF capacitor L- 120 mH inductor Write the impedance Z [Q] equation for the circuit shown in Figure 1. This formula should be in term of the frequency (f), not for angular frequency (). (using MATLAB) 1. From the above formula, plot power factor versus frequency over the frequency range 0 Hz to 1000 Hz. You may use a MATLAB program to do the plotting. 2. Find the frequencies for; Maximum power factor, Minimum power...
Solve the initial value problem honhomogeneous equation: LQ"+RQ+ Q = E. coswt initial Conditions: SQ (0)=Qe, Q (0) = Q! as follows: + First solve the associated homogeneous lequation LQ"+RQ'TEQ =0 by using the characteristic equation Irt art &r=0 to obtain three types of solutions 2 Next show how to find a particular solution Qp to the non homogeneous equation by showing Oplt) = t-Lw²coswt twR sin (wt) ( - Lw²) 4 w²R Eo Show in detail that you can...
3. Show that the differential equation 1 d de sin sin 0 de de sin20 Lastl leads to the associated Legendre equation if we consider the c= cos0, A- v(v+1), ux)-e(0)
(a) For the circuit of Figure 4, assuming a sinusoidal is(t) (0) Prove that the resonant frequeney is given by o- (3 marks) LC (ii) If the total admittance at resonance is 20 ms (seen by the source) with resonant frequency of wo 5000 rad/s and quality factor of Q-10, calculate the values of R L, C, the bandwidth and half-power frequencies in Hertz. (4 marks) VG and hence show (iii) Derive an expression for the driving point impedance Z(jø)...
Problem 2. (1 point) If the differential equation de + 3x = 0 is overdamped, the range of values for mis? Your answer will be an interval of numbers given in the form (1.2) 11.2).(-6), etc.
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
(2 points) Two driven inductors A R = 1 kΩ resistor, a L1 = 20 mH inductor and a L2 28 mH inductor are connected in series. A funtion generator drives the circuit with a 5 Vpp variable frequency sine wave. (a) What is the equivalent impedance Zeq of this circuit? O A. R +jwLIL2/(L1+ L2) E. None of these (b) For what angular frequency does |Zoq v2 R? 20833.3 radians/sec (c) What is the peak-to-peak value of the voltage...
#2 ONLY PLEASE
1. Consider the non-Sturm-Liouville differential equation Multiply this equation by H(x). Determine H(x) such that the equation may be reduced to the standard Sturm-Liouville form: do Given a(z), 3(2), and 7(2), what are p(x), σ(x), and q(x) 2. Consider the eigenvalue problem (a) Use the result from the previous problem to put this in Sturm-Liouville form (b) Using the Rayleigh quotient, show that λ > 0. (c) Solve this equation subject to the boundary conditions and determine...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
Rs 100Ω resistor C- 10 uF capacitor L- 120 mH inductor Write the impedance Z [Q] equation for the circuit shown in Figure 1. This formula should be in term of the frequency (f), not for angular frequency (). (using MATLAB) 1. From the above formula, plot power factor versus frequency over the frequency range 0 Hz to 1000 Hz. You may use a MATLAB program to do the plotting. 2. Find the frequencies for; Maximum power factor, Minimum power...
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