Design a problem to help other students better understand how to determine the Bode magnitude and phase plots of a given transfer function in terms of jÏ. Sketch the Bode magnitude and phase...

Find the transfer function H(s) = V o V i of the circuit shown in Fig. 14.71 . V. ll V, (+)

A radio receiver has an input resistance of 300 . When it is connected directly to an antenna system with a characteristic impedance of 75 , an impedance mismatch occurs. By inserting an...

For the circuit in Fig. 13.82 , determine the impedance seen by the source. j2 N -j1 80/0 V (+ J5 j5 Q j2 Q ell ell

Using Fig. 10.87 , design a problem to help other students better understand the superposition theorem. R2 jXL ll V2 -jXc R1 V, (+1

For the channel designed in Problem 14.32, compute the normal discharge that is expected for a slope of 0.12 percent if the channel is made from painted steel. In Problem Compute the flow area and...

Figure 14.21 represents the approximate shape of a natural stream channel with levees built on either side. The channel is earth with grass cover. Use n = 0.04. If the average slope is 0.000 15,...

Determine the normal discharge for an aluminum rain spout with the shape shown in Fig. 14.19 that runs at the depth of 3.50 in. Use n = 0.013. The spout falls 4 in over a length of 60 ft. 6 in 3.50...

Water is flowing in a formed, unfinished concrete rectangular channel 3.5 m wide. For a depth of 2.0 m, calculate the normal discharge and the Froude number of the flow. The channel slope is 0.1...

Compute the hydraulic radius for the channel shown in Fig. 14.20 if the water depth is 2.50 m. 25 m 0.6 m 0.5 m 1.0 m 2.

Find v(t) for t > 0 in the circuit in Fig. 16.50 . t= 0 1H v = 4 F 10 5 6u(t) A 4.5 A

A series RLC circuit is described by Find the response when L = 0.5H, R = 4Ω, and C = 0.2 F. Let i(0) = 7.5 A and [di(0)/dt] = 0. di(t) , i(t) i(t) = 15 + R- dt dt

A ball of mass 1.5 kg is tied to a string of length 6.0 m as shown in Figure P6.50. The ball is initially hanging vertically and is given an initial velocity of 5.0 m/s in the horizontal direction....

A crate of mass 24 kg is pushed up a friction less ramp by a person as shown in Figure P6.5. Calculate the work done by the person in pushing the crate a distance of 20 m as measured along the ramp....

A rock is thrown horizontally with a speed of 20 m/s from a vertical cliff of height 25 m. (a) How long does it take the rock to reach the horizontal ground below? (b) How far will it land from the...

Using phasors, determine the amplitude and phase of the waveform given by Draw an appropriate diagram. In other words, knowing that Ï(t) = A cos (Ït + α) find A and...

Imagine that we strike two tuning forks, one with a frequency of 340 Hz, the other 342 Hz. What will we hear?

The speed of propagation of a surface wave in a liquid of depth much greater than λ is given by where g = acceleration of gravity, λ = wavelength, Ï = density, Y =...

Show that the group velocity can be written as n + w(dn/dw)

An ionized gas or plasma is a dispersive medium for EM waves. Given that the dispersion equation is where Ï p is the constant plasma frequency, determine expressions for both the phase and group...

The first* experiment directly measuring the bandwidth of a laser (in this case a continuous-wave Pb 0.88 Sn 0.12 Te diode laser) was carried out in 1969. The laser, operating at 0 = 10 600 nm, was...

A 2-in-diameter stream of water having a velocity of 40 ft/s strikes the edge of a flat plate such that half the stream is deflected downward as shown in Fig. 16.16. Calculate the force on the plate...

Calculate the force exerted on a stationary curved vane that deflects a 1-in-diameter stream of water through a 90 angle. The volume flow rate is 150 gal/min.

Compute the hydraulic radius for the channel shown in Fig. 14.20 if the water depth is 0.50 m. 25 m 0.6 m 0.5 m 1.0 m 2.

A fan is rated to deliver 4760 cfm of air at a static pressure of 0.75 in H 2 O. Express the flow rate in m 3 /s and the pressure in Pa.

What is the approximate location of the center of mass of the boomerang in Figure Q7.3? Figure Q7.3 ? y

Two billiard balls undergo an elastic collision as shown in Figure P7.27. Ball 1 is initially traveling along x with a speed of 10 m/s, and ball 2 is at rest. After the collision, ball 1 moves away...

For a given amount of energy to be used for its propulsion, a spacecraft must have much larger tanks than an airplane. Why?

Two particles of mass m 1 = 1.5 kg and m 2 = 3.5 kg undergo a one-dimensional head-on collision as shown in Figure P7.21. Their initial velocities along x are v 1i = 12 m/s and v 2i = -7.5 m/s. The...

A hand grenade is thrown with speed v 0 = 30 m/s, as sketched in Figure P7.51, just prior to exploding. It breaks into two pieces of equal mass after the explosion. One piece has a final velocity of...

A railroad car (m = 3000 kg) is coasting along a level track with an initial speed of 25 m/s. A load of coal is then dropped into the car as sketched in Figure 7.19.? (a) Treat the railroad car plus...

A thin uniform layer of water (n = 1.333) 25.0 nm thick exists on top of a sheet of clear plastic (n = 1.59). At what incident angle will the water strongly reflect blue light (λ 0 = 460...

Sunlight incident on a screen containing two long narrow slits 0.20 mm apart casts a pattern on a white sheet of paper 2.0 m beyond. What is the distance separating the violet ( 0 = 400 nm) in the...

Suppose the separation of the narrow slits in Youngs Experiment is 1.000 mm and the viewing screen is 5.000 m away. Plane waves of monochromatic 589.3-nm light illuminate the slits and the whole...

Use Table 8.6 to derive a Mueller matrix for a half-wave plate having a vertical fast axis. Utilize your result to convert an R-state into an L-state. Verify that the same wave plate will convert an...

Consider a Kerr cell whose plates are separated by a distance d. Let be the effective length of those plates (slightly different from the actual length because of fringing of the field). Show that

Linear light at 135 to the horizontal, oscillating in the second and fourth quadrants, passes through a /2 retarder having its fast axis vertical. Describe the polarization state of the emerging...

The electric-field vector of an incident P-state makes an angle of +30 with the horizontal fast axis of a quarter-wave plate. Describe, in detail, the state of polarization of the emergent wave.

A beam of light is incident normally on a quartz plate whose optic axis is perpendicular to the beam. If 0 = 589.3 nm, compute the wavelengths of both the ordinary and extraordinary waves. What are...

If light that is initially natural and of flux density I i passes through two sheets of HN-32 whose transmission axes are parallel, what will be the flux density of the emerging beam?

Write a MIPS assembly language program for the following pseudocode segment: for(i = 1; i < 100; i++) x(i) = x(i) + x(i-1)

In Section 10.1.3 we talked about introducing an intrinsic phase shift ε between oscillators in a linear array. With this in mind, show that Eq. (10.18) becomes when the incident plane...

(a) Implement an 8-to-1 multiplexer using a minimum number of logic blocks of the type shown in Figure 6-1(a). Give the X and Y functions for each block and show the connections between blocks. (b)...

Design a 4-bit right-shift register using an FPGA with logic blocks as shown in Figure 6-1(a). When the register is clocked, the register loads if Ld = 1 and En = 1; it shifts right when Ld = 0 and...

A narrow single slit (in air) in an opaque screen is illuminated by infrared from a HeNe laser at 1152.2 nm, and it is found that the center of the tenth dark band in the Fraunhofer pattern lies at...

Plane waves from a magnesium lamp ( = 518.36 nm) arrive perpendicularly on an opaque screen containing a long 0.250-mm-wide slit. A large nearby positive lens forms a sharp image of the Fraunhofer...

Realize the SM chart of Problem 5.16 using the two-address microprogramming structure shown in Figure 5-29. (a) Convert the SM chart to the proper form by adding a minimum number of states to the...

Plane waves of green light ( = 546.1 nm) impinge normally on a long narrow slit (0.15 mm wide) in an opaque screen. A large lens with a focal length of +62.0 cm placed just behind the slit produces a...

Consider a tennis ball that is hit by a player at the baseline with a horizontal velocity of 45 m/s (about 100 mi/h). The ball travels as a projectile to the players opponent on the opposite...

A solid wood ball is rotating about an axis that passes through its center. If its angular speed is doubled, (a) by what factor does its rotational kinetic energy change? (b) By what factor does its...

Consider again the cube in Problem 34 (Fig. P8.34), but now assume the force is applied along a horizontal line that is 0.20 m above the floor. At what value of F will the crate begin to tip? Figure...

Four particles with masses m 1 = 15 kg, m 2 = 25 kg, m 3 = 10 kg, and m 4 = 20 kg sit on a very light (mass less) metal sheet and are arranged as shown in Figure P8.42. Find the moment of inertia of...

A string is rolled around a cylinder (m = 4.0 kg) as shown in Figure P8.69. A person pulls on the string, causing the cylinder to roll without slipping along the table. If there is a tension of 30 N...

Make a rough sketch of a possible Fresnel diffraction pattern arising from each of the indicated apertures (Fig. P.10.89). Fig. P.10.89

Suppose the slit in Fig. 10.76 is made very wide. What will the Fresnel diffraction pattern look like? Fig. 10.76 P2 (b) (a)

A bodybuilder is in training and performs curls with a 10-kg barbell to strengthen her biceps muscle. At the top of the stroke, her arm is configured as in Figure P8.79, with her forearm at 35 with...

A somewhat typical person has a total naked area of about 1.4 m 2 and an average skin temperature of 33C. Determine the net power radiated per unit area, the irradiance or more precisely the...

The beam ( = 632.8 nm) from a He-Ne laser, which is initially 3.0 mm in diameter, shines on a perpendicular wall 100 m away. Given that the system is aperture (diffraction) limited, how large is the...

Suppose that a grating spectrometer while in vacuum on Earth sends 500-nm light off at an angle of 20.0 in the first-order spectrum. By comparison, after landing on the planet Mongo, the same light...

A diffraction grating having a mere 50 grooves per cm is the object in the optical computer shown in Fig. 13.41. If it is coherently illuminated by plane waves of green light (543.5 nm) from a He-Ne...

A fine square wire mesh with 50 wires per cm is placed vertically in the object plane of the optical computer of Fig. 13.50. If the lenses each have 1.00-m focal lengths, what must be the...

The water in the pipes of a typical house is at a gauge pressure of 3.0 times atmospheric pressure. What is the absolute pressure in pascals and in units of pounds per square inch?

A diver is swimming at a depth of 10 m. What is the pressure in the water around him?

Consider a fish of average size swimming near the bottom of a lake of depth 20 m. (a) What is the water pressure next to the fish? (b) Estimate the total force exerted by the water on the outside...

Cars use a hydraulic system to transmit the force from the brake pedal to the actual brakes. If this system amplifies the force of your foot by a factor of 10, what is the ratio of the area of the...

A large suitcase full of gold sits at the bottom of a lake. A team of treasure hunters uses a crane to recover the suitcase and finds that a force of 3.0 10 5 N is required to lift the suitcase to...

A beam of collimated polychromatic light ranging from 500 nm to 700 nm impinges normally on a transmission grating having 590 000 lines/m. If the complete second-order spectrum is to appear, how...

Pulmonary surfactant. Oxygen enters the blood in the hollow and roughly spherical alveoli of the lungs. The alveoli are small, approximately 170 mm in radius (Fig. P10.88), yet some 300 million of...

Consider a Fresnel zone plate having a transparent circular disk at its center. This is the m = 1 region, and the tenth transparent region has a diameter of 6.00 mm. Determine the plates principal...

A boy of mass m boy stands at the edge of a merry-go-round of radius R = 3.5 m and mass m mgr , and both are initially at rest. The boy then walks along the edge of the merry-go-round. After walking...

A pencil (mass 10 g and length 15 cm) is initially balanced so that it is sitting vertically on a flat table as shown in Figure P9.26. If the pencil then falls, what is its angular velocity just...

The displacement of a harmonic oscillator is given by y = 9.4 sin(15t), where the units of y are meters and t is measured in seconds. What is its maximum velocity?

A child plays on a bungee cord and oscillates with a certain frequency f. An adult with a mass that is five times greater than that of the child then uses the same bungee cord. What is the ratio of...

A mass-on-a-spring system has spring constant k = 400 N/m and mass m = 0.50 kg. (a) If it is given an initial displacement of 0.25 m and then released, what is the initial potential energy of the...

A car mounted on struts is like a mass on a spring. If you ignore damping, how will the frequency of the oscillations change if passengers (or a heavy load) are added to the car? Will the frequency...

When a group of marching soldiers reach a bridge, they often break stride and do not walk in step across the bridge. Explain why.

A simple pendulum has a length of 2.5 m and is pulled a distance y = 0.25 m to one side and then released (Fig. P11.24).? Figure P11.24 ? (a) What is the speed of the pendulum when it passes through...

Consider a simple pendulum with L = 1.2 m and m = 2.0 kg. Suppose the mass is initially at rest at the lowest point on its trajectory when it is given an impulse such that it then has a velocity of...

A simple pendulum has a length L and a mass m. At its highest point, the pendulum mass is 0.25L above its lowest point (Fig. P11.42). What is the speed of the mass when it is at its lowest point?...

Figure P11.62 shows the amplitude as a function of frequency for a driven, damped oscillator. Estimate the resonant frequency. Figure P11.62 ? 500 1000 1500 Frequency (Hz) Amplitude (mm)

Electrical power produced by a wind turbine. The force of the wind on the blades of a wind turbine (Fig. 9.4A) is proportional to v 2 , where v is the speed of the wind (Chapter 3). The angular...

A wave on a string is described by the equation y = (4.2 mm cos(3000t - 0.45x), where t is measured in s and x is measured in mm. Make a graph of the displacement of the string at x = 0.35 mm as a...

Consider a guitar string that has a tension of 90 N, a length of 65 cm, and a mass per unit length of 7.9 10 4 kg/m. What is the fundamental frequency of the string? That is, what is the frequency...

Suppose the sound intensity level 0.10 m from a loudspeaker is 110 dB. Assuming the speaker generates wave fronts that have a hemispherical shape (Fig. P13.25), what is the intensity 5.5 m from the...

A sound wave has an intensity of 2.5 10 -3 W/m 2 . What is the intensity level in decibels?

Use the general relation for the speed of sound in Equation 13.3 together with the ideal gas law (see Chapter 15 if you need a refresher on the ideal gas law) to show that the speed of sound in a gas...

Suppose a sound wave in air at room temperature has a wavelength of 400 m. What is its frequency?

Rank each substance according to how fast sound travels in that medium, from that with the largest velocity to that with the slowest. (a) Air (b) Water (c) Steel (d) Aluminum

A child drops a rock into a vertical mine shaft that is precisely 406 m deep. The sound of the rock hitting the bottom of the shaft is heard 10.3 s after the child drops the rock. What is the...

You are given the job of designing a bridge that is to be made of concrete slabs that rest on a steel support frame. The total length of the bridge is 300 m, and you want to be sure that the...

Two identical particles carrying equal charge are moving in opposite directions, perpendicular to a uniform magnetic field, when they collide elastically head-on. Describe their subsequent motion.

Explain how two objects can be attracted due to an electric force, even when one object has zero net charge.

A piece of amber is charged by rubbing with a piece of fur. If the net excess charge on the fur is +8.5 nC (+8.5 10 -9 C), how many electrons were added to the amber?

Two point charges are separated by a distance r. If the separation is reduced by a factor of 1.5, by what factor does the electric force between them change?

A helium nucleus contains two protons. What is the approximate magnitude of the electric force between these two protons? Is this force attractive or repulsive? The radius of this nucleus is about...

What is the magnitude of the electric field at a distance of 1.5 m from a point charge with Q = 3.5 C?

An electron is traveling through a region of space in which the electric field is along the +x direction and has a magnitude of 2000 N/C. What is the acceleration of the electron? Give both the...

An electron gun in the picture tube of a CRT accelerates electrons from rest to a speed of 4.0 10 7 m/s along a distance of 1.0 cm. What is the magnitude of the uniform electric field used by the...

An electric dipole is situated as shown in Figure P17.31, and the dipole charges are Q, with Q = 3.3 C. A point particle with charge q is now placed at location A as shown in the figure. If the force...

A small, plastic sphere of mass m = 100 g is attached to a string as shown in Figure P17.45. There is an electric field of 100 N/C directed along the +x direction. If the string makes an angle ? =...