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2. Hecht problem 9.54: Given that the mirrors of a Fabry Perot Interferometer have an amplitude...
8. A Fabry-Perot interferometer consists of two mirrors, each with a reflection coefficient R of 0.95, that are sepa...
8. A Fabry-Perot interferometer consists of two mirrors, each with a reflection coefficient R of 0.95, that are separated by a distance d in air. The transmission property of the interferometer is described by the Airy's formula, which is given by I-sin 1+Fsin) Here, is the transmitted light intensity due to an input light intensity of . F is the coefficient of finesse that is given by F#-A-, and is the phase difference between (1-R) successive reflections. The interferometer is...
Chapter 31, Problem 047 An RLC circuit such as that of Figure (a) has R =...
Chapter 31, Problem 047 An RLC circuit such as that of Figure (a) has R = 5.62 2, C = 25.2 F, L = 1.47 H, and Em = 38.0 V. (a) At what angular frequency we will the current amplitude have its maximum value, as in the resonance curves of Figure (b)? (b) What is this maximum value? At what (c) lower angular frequency wd1 and (d) higher angular frequency w d2 will the current amplitude be half this...
PAINTEA VELISION BACK NEXT Chapter 34, Problem 022 GO More mirrors. Object O stands on the central axis of a spheri...
PAINTEA VELISION BACK NEXT Chapter 34, Problem 022 GO More mirrors. Object O stands on the central axis of a spherical or plane mirror. For this situation (see the table below, all distances are in centimeters, the given value of is a magnitude with unknown sign), find (a) the type of mirror, (b) the radius of curvaturer (nonzero number or if Infinity), (c) the object distance p. (d) the image distance I, whether (e) the image is real or virtual,...
Problem 5 (40 pts). Given the system of nonlinear differential equations Se=y+ 2(x2 + y2 -...
Problem 5 (40 pts). Given the system of nonlinear differential equations Se=y+ 2(x2 + y2 - 1) y'= -r + y(x² + y2 - 1) (a) Find its critical point(s). (b) Linearize the system about each critical point. (c) Classify each critical point by discussing the zeros of the corresponding characteristic equa- tion. (d) Solve the linearized systems of differential equations about the critical point(s).
16. Problem 16. Consider a composite system characterized by a joint probability density function given by, def The constant ξ is a real normalization factor and pxy is defined on the two-dimensi...
16. Problem 16. Consider a composite system characterized by a joint probability density function given by, def The constant ξ is a real normalization factor and pxy is defined on the two-dimensional planar region DCartesian def where Rt denotes the set of strictly positive real numbers. a) Define the set Dpolar representing DCartesian recast in polar coordinates (r, ); b) Performing a change of coordinates (namely, from Cartesian to polar coordinates), find the expression of the new joint probability density...
I need help solving this problem using Python. 2. Given f(x) = (cos(x))2 and g(x)-(cos(x))2: ππ...
I need help solving this problem using Python.
2. Given f(x) = (cos(x))2 and g(x)-(cos(x))2: ππ (a) Plot the functions on the x-interval | and the line x = π on the same set of axes. (b) Find the volume when the right half of the region between the curves (on x є |0, | ) is rotated about the y-axis. (c) Find the volume when the top half of the region is rotated about the r-axis. (d) Find the...
Consider the standard two-periods consumption model where consumers have the utility func- tion u(c)-S Furthermore, let...
Consider the standard two-periods consumption model where consumers have the utility func- tion u(c)-S Furthermore, let a =0, y 0,and y-1. where 0 < ? and ? > 1 are parameters (a) Write down the consumer problem (b) Find the first order conditions. (c) Find the optimal consumption plan (c and c as function of variables ans parameters "given" to the consumer) Set ?-05, ? (d) (e) Set ?-2, ?-0.5 and r-0.02. Which consumption is larger, present or future? why?...
Last Name: Page Problem #2 (35 Points) Given The motion of a particle P which coincides with the ...
Last Name: Page Problem #2 (35 Points) Given The motion of a particle P which coincides with the robot's gripper hand at point A is defined by the relations where t is expressed in seconds. Please note that kı, k2, and ks are constants which are greater than zero. For the initial condition, the particle has an angle of 0-0° when-0 sec. So, when t 2 sec, Find: a) The "script" values for radial and transverse coordinates, that is, r,t,i,...
Name: Problem 2. (Option # 1 ) Five half wavelength dipole antennas are used as sources to form a linear phased arr...
Name: Problem 2. (Option # 1 ) Five half wavelength dipole antennas are used as sources to form a linear phased array antenna, as shown below. These elements are all excited by sinusoidal current source of equal amplitude and phase followed by phase shifters. (9 pts.) a) If d 2, write the expression for array factor of the linear array. (9 pts.) b) Find total field at observation point P: (r, 0, 6) at far-field (i.e., kr>1). (8 pts.) c)...
Problem 2: (a) Suppose you are given the differential equation Divide the equation be u and...
Problem 2: (a) Suppose you are given the differential equation Divide the equation be u and rescale time to show this can be written as Give the expression for t and λ in terms of t, wo and wi. (b) Assuming λ « 1, write the solution of the formiz(t)-Σοοολ"rn(t). Plugging this into equation (5), show you can write the equation as Σλ"(afr" + r"-Σ ntEn- r.r.)=0 46m-1 (c) Assume that each term in the sum over n must separately...
8. A Fabry-Perot interferometer consists of two mirrors, each with a reflection coefficient R of 0.95, that are separated by a distance d in air. The transmission property of the interferometer is described by the Airy's formula, which is given by I-sin 1+Fsin) Here, is the transmitted light intensity due to an input light intensity of . F is the coefficient of finesse that is given by F#-A-, and is the phase difference between (1-R) successive reflections. The interferometer is...
Chapter 31, Problem 047 An RLC circuit such as that of Figure (a) has R = 5.62 2, C = 25.2 F, L = 1.47 H, and Em = 38.0 V. (a) At what angular frequency we will the current amplitude have its maximum value, as in the resonance curves of Figure (b)? (b) What is this maximum value? At what (c) lower angular frequency wd1 and (d) higher angular frequency w d2 will the current amplitude be half this...
PAINTEA VELISION BACK NEXT Chapter 34, Problem 022 GO More mirrors. Object O stands on the central axis of a spherical or plane mirror. For this situation (see the table below, all distances are in centimeters, the given value of is a magnitude with unknown sign), find (a) the type of mirror, (b) the radius of curvaturer (nonzero number or if Infinity), (c) the object distance p. (d) the image distance I, whether (e) the image is real or virtual,...
Problem 5 (40 pts). Given the system of nonlinear differential equations Se=y+ 2(x2 + y2 - 1) y'= -r + y(x² + y2 - 1) (a) Find its critical point(s). (b) Linearize the system about each critical point. (c) Classify each critical point by discussing the zeros of the corresponding characteristic equa- tion. (d) Solve the linearized systems of differential equations about the critical point(s).
16. Problem 16. Consider a composite system characterized by a joint probability density function given by, def The constant ξ is a real normalization factor and pxy is defined on the two-dimensional planar region DCartesian def where Rt denotes the set of strictly positive real numbers. a) Define the set Dpolar representing DCartesian recast in polar coordinates (r, ); b) Performing a change of coordinates (namely, from Cartesian to polar coordinates), find the expression of the new joint probability density...
I need help solving this problem using Python.
2. Given f(x) = (cos(x))2 and g(x)-(cos(x))2: ππ (a) Plot the functions on the x-interval | and the line x = π on the same set of axes. (b) Find the volume when the right half of the region between the curves (on x є |0, | ) is rotated about the y-axis. (c) Find the volume when the top half of the region is rotated about the r-axis. (d) Find the...
Consider the standard two-periods consumption model where consumers have the utility func- tion u(c)-S Furthermore, let a =0, y 0,and y-1. where 0 < ? and ? > 1 are parameters (a) Write down the consumer problem (b) Find the first order conditions. (c) Find the optimal consumption plan (c and c as function of variables ans parameters "given" to the consumer) Set ?-05, ? (d) (e) Set ?-2, ?-0.5 and r-0.02. Which consumption is larger, present or future? why?...
Last Name: Page Problem #2 (35 Points) Given The motion of a particle P which coincides with the robot's gripper hand at point A is defined by the relations where t is expressed in seconds. Please note that kı, k2, and ks are constants which are greater than zero. For the initial condition, the particle has an angle of 0-0° when-0 sec. So, when t 2 sec, Find: a) The "script" values for radial and transverse coordinates, that is, r,t,i,...
Name: Problem 2. (Option # 1 ) Five half wavelength dipole antennas are used as sources to form a linear phased array antenna, as shown below. These elements are all excited by sinusoidal current source of equal amplitude and phase followed by phase shifters. (9 pts.) a) If d 2, write the expression for array factor of the linear array. (9 pts.) b) Find total field at observation point P: (r, 0, 6) at far-field (i.e., kr>1). (8 pts.) c)...
Problem 2: (a) Suppose you are given the differential equation Divide the equation be u and rescale time to show this can be written as Give the expression for t and λ in terms of t, wo and wi. (b) Assuming λ « 1, write the solution of the formiz(t)-Σοοολ"rn(t). Plugging this into equation (5), show you can write the equation as Σλ"(afr" + r"-Σ ntEn- r.r.)=0 46m-1 (c) Assume that each term in the sum over n must separately...
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