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1 Million+ Step-by-step solutions * Q:Use the impedance method to obtain the transfer function Vo(s)/Vs(s)Use the impedance method to obtain the transfer function Vo(s)/Vs(s) for the circuit shown in Figure.*

Q:Use the impedance method to obtain the transfer function Vo(s)/Vs(s)Use the impedance method to obtain the transfer function Vo(s)/Vs(s) for the circuit shown in Figure.

Q:Use the impedance method to obtain the transfer function Vo(s)/Vs(s)Use the impedance method to obtain the transfer function Vo(s)/Vs(s) for the circuit shown in Figure.

Q:Draw a block diagram of the circuit shown in Figure.Draw a block diagram of the circuit shown in Figure. The inputs are v1 and v2- The output is i2.

Q:Draw a block diagram of the circuit shown in Figure.Draw a block diagram of the circuit shown in Figure. The inputs are v1 and v2 – The output is v3.

Q:Obtain the transfer function Vo(s)/Vi{s) for the op-amp system shownObtain the transfer function Vo(s)/Vi{s) for the op-amp system shown in Figure.

Q:The Wheatstone bridge, like that shown in Figure, is usedThe Wheatstone bridge, like that shown in Figure, is used for various measurements. For example, a strain gage sensor utilizes the fact that the resistance of wire changes when deformed. If the sensor is one resistance leg of the bridge, then the deformation can be determined from the voltage v1. Determine the relation between the voltage v1 and the supply voltage vs.

Q:Obtain the transfer function Vo(s)/Vi(s) for the op-amp system shownObtain the transfer function Vo(s)/Vi(s) for the op-amp system shown in Figure.

Q:Obtain the transfer function Vo(s)/Vi(s) for the op-amp system shownObtain the transfer function Vo(s)/Vi(s) for the op-amp system shown in Figure.

Q:Obtain the transfer function Vo(s)/Vi, (s) for the op-amp systemObtain the transfer function Vo(s)/Vi, (s) for the op-amp system shown in Figure.

Q:Obtain the transfer function Vo(s)/Vi(s) for the op-amp system shownObtain the transfer function Vo(s)/Vi(s) for the op-amp system shown in Figure

Q:(a) Obtain the transfer function Ɵ(s)/Vi(s) for the D’Arsonval meter, (b)(a) Obtain the transfer function Ɵ(s)/Vi(s) for the D’Arsonval meter,

(b) Use the final value theorem to obtain the expression for the steady-state value of the angle θ if the applied voltage vi, is a step function.

Q:(a) Obtain the transfer function Ω(s)/TL(s) for the field-controlled motor (a) Obtain the transfer function Ω(s)/TL(s) for the field-controlled motor of Example 6.5.2.

(b) Modify the field-controlled motor model in Example 6.5.2 so that the output is the angular displacement θ, rather than the speed ω, where ω = θ. Obtain the transfer functions Ɵ(s)/Vf (s) and Ɵ(s)TL(s).

Q:Modify the motor model given in Example 6.5.2 to accountModify the motor model given in Example 6.5.2 to account for a gear pair between the motor shaft and the load. The ratio of motor speed to load speed ωL is N. The motor inertia is lm and the motor damping is cm. The load inertia is IL, and the load damping is cL. The load torque TL. acts directly on the load inertia. Obtain the transfer functions ΩL(s)/Vf(s) and ΩL(S)/TL(S).

Q:The derivation of the field-controlled motor model in Section 6.5The derivation of the field-controlled motor model in Section 6.5 neglected the elasticity of the motor-load shaft. Figure shows a model that includes this elasticity, denoted by its equivalent torsional spring constant kT. The motor inertia is I1, and the load inertia is l2. Derive the differential equation model with Î¸2 as output and vf as input.

Q:Figure is the circuit diagram of a speed-control system inFigure is the circuit diagram of a speed-control system in which the dc motor voltage va is supplied by a generator driven by an engine. This system has been used on locomotives whose diesel engine operates most efficiently at one speed. The efficiency of the electric motor is not as sensitive to speed and thus can be used to drive the locomotive at various speeds. The motor voltage va is varied by changing the generator input voltage vf. The voltage va is related to the generator field current if by va = Kfif.

Derive the system model relating the output speed Ï to the voltage vf, and obtain the transfer function Î©(s)/ Vf(s).

Q:The parameter values for a certain armature-controlled motor are KT =The parameter values for a certain armature-controlled motor are

KT = Kb = 0.2 N.m/A

c = 5 x 10-4 N.m-s/rad

Ra = 0:8Ω

The manufacturer’s data states that the motor’s maximum speed is 3500 rpm, and the maximum armature current it can withstand without demagnetizing is 40 A.

Compute the no-load speed, the no-load current, and the stall torque. Determine whether the motor can be used with an applied voltage of va = 15 V.

Q:The power supply of the circuit showed in Figure suppliesThe power supply of the circuit showed in Figure supplies a voltage of 9V. Compute the current i and the power P that must be supplied.

Q:The parameter values for a certain armature-controlled motor are KT =The parameter values for a certain armature-controlled motor are

KT = Kb = 0.05 N.m/A

Ra = 0.8 Ω

La = 3x 10-3 H

I = 8 x 10-5 kg.m2

Where I includes the inertia of the armature and that of the load investigate the effect of the damping constant c on the motor’s characteristic roots and on its response to a step voltage input. Use the following values of c (in N.m.s/rad): c = 0,c = 0.01, and c = 0.1. For each case, estimate how long the motor’s speed will take to become constant, and discuss whether or not the speed will oscillate before it becomes constant.

Q:The parameter values for a certain armature-controlled motor are KT =The parameter values for a certain armature-controlled motor are

KT = Kb = 0.2 N . m/A

c = 5 x 10-4 N-m-s/rad

Ra = 0.8 Ω

La 4 x l0-3 H

I = 5 x 10-4 kg-m2

Where c and I include the effect of the load

Obtain the step response of ia(t) and ω(t) if the applied voltage is va = 10V.

Obtain the step response of ia(t) and ω (t) if the load torque is TL = 0.2 N.m.

Q:The following measurements were performed on a permanent magnet motorThe following measurements were performed on a permanent magnet motor when the applied voltage was va = 20 V. The measured stall current was 25 A. The no-load speed was 2400 rpm and the no-load current was 0.6 A. Estimate the values of Kb, KT, Ra, and c.

Q:A single link of a robot arm is shown inA single link of a robot arm is shown in Figure. The arm mass is m and its center of mass is located a distance L from the joint, which is driven by a motor torque Tm through spur gears. Suppose that the equivalent inertia felt at the motor shaft is 0.215 kg.m2. As the arm rotates, the effect of the arm weight generates an opposing torque that depends on the arm angle, and is therefore nonlinear. For this problem, however, assume that the effect of the opposing torque is a constant 4.2 N .m at the motor shaft. Neglect damping in the system. It is desired to have the motor shaft rotate through 3Ï/4 rad in a total time of 2 s, using a trapezoidal speed profile with t1 = 0.3 s and t2 = 1.7 s.

The given motor parameters are Ra= 4 Î©, La = 3 x 10-3 H, and KT = 0.3 N.m/A. Compute the energy consumption per cycle; the maximum required torque, current, and voltage; the rms torque; and the rms current.

Q:A conveyor drive system to produce translation of the loadA conveyor drive system to produce translation of the load is shown in Figure. Suppose that the equivalent inertia felt at the motor shaft is 0.05 kg.m2, and that the effect of Coulomb friction in the system produces an opposing torque of 3.6 N.m at the motor shaft. Neglect damping in the system. It is desired to have the motor shaft rotate through 11 revolutions in a total time of 3 s, using a trapezoidal speed profile with t1 = 0.5 s and t2 = 2.5 s.

The given motor parameters are Ra = 3Î©, La = 4 x 10-3 H, and KT = 0.4N.m/A. Compute the energy consumption per cycle; the maximum required torque, current, and voltage; the rms torque; and the rms current.

Q:Consider the accelerometer model in Section 6.7. Its transfer functionConsider the accelerometer model in Section 6.7. Its transfer function can be expressed as

Y(s)/ Z(s) = -s2/(s2 + (c/m)s + k/m)

Suppose that the input displacement is z(t) = 10 sin 120/ mm. Consider two cases, in SI units:

(a) k/m = 100 and c/m = 18

(b) k/m = 106 and c/m = 1800.

Obtain the steady-state response y(t) for each case. By comparing the amplitude of y(t) with the amplitudes of z(t) and (t), determine which case can be used as a vibrometer (to measure displacement) and which can be used as an accelerometer (to measure acceleration).

Q:An electromagnetic microphone has a construction similar to that ofAn electromagnetic microphone has a construction similar to that of the speaker shown in Figure 6.7.2, except that there is no applied voltage and the sound waves are incoming rather than outgoing. They exert a force fs on the diaphragm whose mass is m, damping is c, and stiffness is k. Develop a model of the microphone, whose input is fs, and output is the current i in the coil.

Q:Consider the speaker model developed in Example 6.7.1. The model,Consider the speaker model developed in Example 6.7.1. The model, whose transfer function is given by equation (3) in that example, is third order and therefore we cannot obtain a useful expression for the characteristic roots. Sometimes inductance L and damping c are small enough to be ignored. If L = 0, the model becomes second order,

(a) Obtain the transfer function X(s)/V(s) for the case where L = c = 0, and obtain the expressions for the two roots,

(b) Compare the results with the third-order case where

m = 0.002 kg

k = 4 x 105 N/m

Kf = 16N/A

Kb = 13 V.s/m

R = 12Ω

L = 10-3 H

C = 0

Q:The parameter values for a certain armature-controlled motor are KTThe parameter values for a certain armature-controlled motor are

KT = Kb = 0.2 N.m/A

c = 5 x 10-4 N.m.s/rad

Rb = 0.8Ω

La = 4 x 10-3 H

I = 5 x 10-4 kg.m2

Where c and I include the effect of the load the load torque is zero. Use MATLAB to obtain a plot of the step response of ia(t) and ω(t) if the applied voltage is va = 10 V. Determine the peak value of ia(t).

Q:Consider the motor whose parameters are given in Problem 48.Consider the motor whose parameters are given in Problem 48. Use MATLAB to obtain a plot of the response of ia(t) and ω(t) if the applied voltage is the modified step va(t) = 10(1 – e-100t) V. Determine the peak value of ia(t).

In Problem 48

KT = Kb = 0.2 N.m/A

c = 5 x 10-4 N.m.s/rad

Rb = 0.8Ω

La = 4 x 10-3 H

I = 5 x 10-4 kg.m2

Q:Obtain the model of the voltage v1, given the currentObtain the model of the voltage v1, given the current is, for the circuit shown in Figure.

Q:Consider the circuit shown in Figure. The parameter values areConsider the circuit shown in Figure. The parameter values are R = 103 Î©, C = 2 x 10-6 F, and L = 2 x 10-3 H. The voltage v1 is a step input of magnitude 5 V, and the voltage v2 is sinusoidal with frequency of 60 Hz and amplitude of 4 V. The initial conditions are zero. Use MATLAB to obtain a plot of the current response hit).

Q:The parameter values for a certain armature-controlled motor are KT =The parameter values for a certain armature-controlled motor are

KT = Kb = 0.2 N.m/A

c = 3 x 10-4 N.m.s/rad

Ra = 0.8 Ω

La = 4xl0-3H

I = 4 x I0-4 kg-m2

The system uses a gear reducer with a reduction ratio of 3:1. The load inertia is 10-3 kg.m2, the load torque is 0.04 N.m, and the load damping constant is 1.8 x 10-3 N-m-s/rad.

Use MATLAB to obtain a plot of the step response of ia(t) and ω(t) if the applied voltage is va = 20 V. Determine the peak value of ia(t).

Q:The parameter values for a certain armature-controlled motor are KT =The parameter values for a certain armature-controlled motor are

KT = Kb = 0.05 N.m/A

c = 0

Ra = 0.8 Î©

La = 3 x l0-3 H

I = 8 x l0-5 kg.m2

Where I include the inertia of the armature and that of the load the load torque is zero. The applied voltage is a trapezoidal function defined as follows.

Use MATLAB to obtain of plot of the response of ia(t) and Ï(t).

Compute the energy consumption per cycle; the maximum required torque, current, and voltage; the rms torque; and the rms current.

Q:A single link of a robot arm is shown inA single link of a robot arm is shown in Figure. The arm mass is m and its center of mass is located a distance L from the joint, which is driven by a motor torque Tm through spur gears. Suppose that the equivalent inertia felt at the motor shaft is 0.215 kg.m2. As the arm rotates, the effect of the arm weight generates an opposing torque that depends on the arm angle, and is therefore nonlinear. The effect of the opposing torque at the motor shaft is 4.2 sin Î¸ N.m. Neglect damping in the system. It is desired to have the motor shaft rotate through 3Ï/4 rad in a total time of 2 s, using a trapezoidal speed profile with t1 = 0.3 s and t2 = 1.7 s.

The given motor parameters are Ra = 4 Î©, La = 3 x 10-3 H, and KT = 0.3 N.m/A. Use MATLAB to obtain of plot of the response of the motor current and the motor speed.

Q:Consider the circuit shown in Figure. The parameter values areConsider the circuit shown in Figure. The parameter values are R = 104 Î©, C = 2 x 10-6 F, and L = 2 x 10-3 H. The voltage v1 is a single pulse of magnitude 5 V and duration 0.05 s, and the voltage v2 is sinusoidal with frequency of 60 Hz and amplitude of 4 V. The initial conditions are zero. Use Simulink to obtain a plot of the current response i3(t).

Q:Consider the circuit shown in Figure. The parameter values areConsider the circuit shown in Figure. The parameter values are R = 2 x 104 Î© and C = 3 x 10-6 F. The voltage vs is vs(t) = 12us (t) + 3 sin 120ÏtV. The initial conditions are zero. Use Simulink to obtain a plot of the responses vo(t) and v1(t).

Q:The parameter values for a certain armature-controlled motor are KT =The parameter values for a certain armature-controlled motor are

KT = Kb = 0.2 N.m/A

c = 5 x 10-4 N.m.s/rad

Ra = 0.8 Ω

La = 4 x 10-3 H

I = 5 x 10-4 kg.m2

Where c and / include the effect of the load. The load torque is zero.

a. Use Simulink to obtain a plot of the step response of the motor torque and speed if the applied voltage is va = 10 V. Determine the peak value of the motor torque.

b. Now suppose that the motor torque is limited to one-half the peak value found in part (a). Use Simulink to obtain a plot of the step response of the motor torque and speed if the applied voltage is va = 10 V.

Q:The parameter values for a certain armature-controlled motor are KT =The parameter values for a certain armature-controlled motor are

KT = Kb = 0.05 N.m/A

c = 0

Ra= 0.8 Î©

La = 3 x 10-3 H

I = 8 x 10-5 kg.m2

Where I include the inertia of the armature and that of the load the load torque is zero. The applied voltage is a trapezoidal function defined as follows.

A trapezoidal profile can be created by adding and subtracting ramp functions starting at different times. Use several Ramp source blocks and Sum blocks in Simulink to create the trapezoidal input. Obtain a plot of the response of ia(t) and Ï(t).

Q:(a) Obtain the model of the voltage vo, given the(a) Obtain the model of the voltage vo, given the supply voltage vs, for the circuit shown in Figure.

(b) Suppose vs(t) = Vus(t). Obtain the expressions for the free and forced responses for v”(t).

Q:(a) Obtain the model of the voltage vo, given the(a) Obtain the model of the voltage vo, given the supply voltage vs for the circuit shown in Figure

(b) Suppose vs(t) = Vus(t). Obtain the expressions for the free and forced responses for vo(t).

Q:(a) The circuit shown in Figure is a model of(a) The circuit shown in Figure is a model of a solenoid, such as that used to engage the gear of a car’s starter motor to the engine’s flywheel. The solenoid is constructed by winding wire around an iron core to make an electromagnet. The resistance R is that of the wire, and the inductance L is due to the electromagnetic effect. When the supply voltage vs is turned on, the resulting current activates the magnet, which moves the starter gear. Obtain the model of the current i given the supply voltage vs.

(b) Suppose vs(t) = Vus(t) and i(0) = 0. Obtain the expression for the response for i(t).

Q:For the hydraulic system shown in Figure, given A1 =For the hydraulic system shown in Figure, given A1 = 10 in.2, A2 = 30 in.2, and mg = 60 lb, find the force f1 required to lift the mass m a distance x2 = 6 in. Also find the distance x1 and the work done by the force f1.

Q:Consider the cylindrical tank shown in Figure. Derive the dynamicConsider the cylindrical tank shown in Figure. Derive the dynamic model of the height h, assuming that the input mass flow rate is qm(t).

Q:Consider the tank shown in Figure. Derive the dynamic modelConsider the tank shown in Figure. Derive the dynamic model of the height h, assuming that the input mass flow rate is qm (t).

Q:Air flows in a certain cylindrical pipe 1 m longAir flows in a certain cylindrical pipe 1 m long with an inside diameter of 1 mm. The pressure difference between the ends of the pipe is 0.1 atm. Compute the laminar resistance, the Reynolds number, the entrance length, and the mass flow rate. Comment on the accuracy of the resistance calculation. For air use μ = 1.58 x 10-5 N.s/m2 and ( = 1.2885 kg/m3.

Q:Derive the expression for the linearized resistance due to orificeDerive the expression for the linearized resistance due to orifice flow near a reference height h.

Q:Consider the cylindrical container treated in Example 7.4.3. Suppose theConsider the cylindrical container treated in Example 7.4.3. Suppose the outlet flow is turbulent. Derive the dynamic model of the system

(a) In terms of the gage pressure p at the bottom of the tank

(b) In terms of the height h.

Q:A certain tank has a bottom area A = 20A certain tank has a bottom area A = 20 m2. The liquid level in the tank is initially 5 m. When the outlet is opened, it takes 200 s to empty by 98%.

a. Estimate the value of the linear resistance R.

b. Find the steady-state height if the inflow is q = 3 m3/s.

Q:A certain tank has a circular bottom area A =A certain tank has a circular bottom area A = 20 ft2. It is drained by a pipe whose linear resistance is R = 150 m-1sec-1. The tank contains water whose mass density is 1.94 slug/ft3

a. Estimate how long it will take for the tank to empty if the water height is initially 30 ft.

b. Suppose we dump water into the tank at a rate of 0.1 ft3/sec. If the tank is initially empty and the outlet pipe remains open, find the steady-state height and the time to reach one-third that height, and estimate how long it will take to reach the steady-state height.

Q:The water inflow rate to a certain tank was keptThe water inflow rate to a certain tank was kept constant until the water height above the orifice outlet reached a constant level. The inflow rate was then measured, and the process repeated for a larger inflow rate. The data are given in the table. Find the effective area CdAo” for the tank’s outlet orifice.

Inflow rate (liters/min)Liquid height (cm)

98 ………………………………. 30

93 ………………………………. 27

91 ………………………………. 24

86 ………………………………. 21

81 ………………………………. 18

75 ………………………………. 15

68 ………………………………. 12

63 ………………………………. 9

56 ………………………………. 6

49 ………………………………. 3

Q:In the system shown in Figure, a component such asIn the system shown in Figure, a component such as a valve has been inserted between the two lengths of pipe. Assume that turbulent flow exists throughout the system. Use the resistance relation 7.3.7.

(a) Find the total turbulent resistance,

(b) Develop a model for the behavior of the liquid height h, with the mass flow rate qmi as the input.

Q:The cylindrical tank shown in Figure 7.4.3 has a circularThe cylindrical tank shown in Figure 7.4.3 has a circular bottom area A. The mass inflow rate from the flow source is qmi(t), a given function of time. The flow through the outlet is turbulent, and the outlet discharges to atmospheric pressure pa. Develop a model of the liquid height h.

Q:Refer to the water storage and supply system shown inRefer to the water storage and supply system shown in Figure 7.1.2. The cylindrical tank has a radius of 11 ft, and the water height is initially 5 ft. Find the water height after 5 hr if 1000 gallons per minute are pumped out of the well and 800 gallons per minute are withdrawn from the tank. 1 gallon is 0. T3368 ft3.

Q:In the liquid level system shown in Figure, the resistancesIn the liquid level system shown in Figure, the resistances R1 and R2 are linear, and the input is the pressure source ps. Obtain the differential equation model for the height h, assuming that > D.

Q:The water height in a certain tank was measured atThe water height in a certain tank was measured at several times with no inflow applied. See Figure 7.4.3. The resistance R is a linearized resistance. The data are given in the table. The tank’s bottom area is A = 6 ft2,

a. Estimate the resistance R.

b. Suppose the initial height is known to be exactly 20.2 ft. How does this change the results of part (a)?

Time (sec) Height (ft)

0……………………………… 20.2

300………………………….17.26

600…………………………..14.6

900…………………………..12.4

1200………………………….10.4

1500………………………….9.0

1800………………………….7.6

2100………………………….6.4

2400………………………….5.4

Q:Derive the model for the system shown in Figure. TheDerive the model for the system shown in Figure. The flow rate mi is a mass flow rate and the resistances are linearized.

Q:(a) Develop a model of the two liquid heights in(a) Develop a model of the two liquid heights in the system shown in Figure. The inflow rate qmi(t) is a mass flow rate,

(b) Using the values R1 = R, R2 = 3R, A1 = A, and A2 = 4A, find the transfer function H2(s)/Qmi(s).

Q:Consider Example 7.4.6. Suppose that R1 = R, R2 =Consider Example 7.4.6. Suppose that R1 = R, R2 = 3R, A1 = A, and A2 = 2A. Find the transfer function H1(s)/Qmi(s) and the characteristic roots.

Q:Design a piston-type damper using an oil with a viscosityDesign a piston-type damper using an oil with a viscosity at 20°C of μ = 0.9 kg/(m.s). The desired damping coefficient is 2000 N.s/m. See Figure 7.4.4.

Q:For the damper shown in Figure 7.4.7, assume that theFor the damper shown in Figure 7.4.7, assume that the flow through the hole is turbulent, and neglect the term m. Develop a model of the relation between the force f and , the relative velocity between the piston and the cylinder.

Q:An electric motor is sometimes used to move the spoolAn electric motor is sometimes used to move the spool valve of a hydraulic motor. In Figure the force f is due to electric motor acting through a rack-and-pinion gear. Develop a model of the system with the load displacement y as the output and the force f as the input. Consider two cases:

(a) m1 = 0

(b) m1 â 0.

Q:In Figure the piston of area A is connected toIn Figure the piston of area A is connected to the axle of the cylinder of radius R, mass in, and inertia I about its center. Develop a dynamic model of the axle’s translation x, with the pressures p1 and p2 as the inputs.

Q:Figure shows a pendulum driven by a hydraulic piston. AssumingFigure shows a pendulum driven by a hydraulic piston. Assuming small angles Î¸ and a concentrated mass in a distance L1 from the pivot, derive the equation of motion with the pressures p1 and p2 as inputs.

Q:Consider the piston and mass shown in Figure 7.1.4a. SupposeConsider the piston and mass shown in Figure 7.1.4a. Suppose there is dry friction acting between the mass m and the surface. Find the minimum area A of the piston required to move the mass against the friction force μmg, where μ = 0.6, mg = 1000 N, p1 = 3 x 105 Pa, and p2 = 105 Pa.

Q:Figure shows an example of a hydraulic accumulator, which isFigure shows an example of a hydraulic accumulator, which is a device for reducing pressure fluctuations in a hydraulic line or pipe. The fluid density is (, the plate mass is m, and the plate area is A. Develop a dynamic model of the pressure p with the pressures p1 and p2 as the given inputs. Assume that m of the plate is small, and that the hydrostatic pressure (gh is small.

Q:Design a hydraulic accumulator of the type shown in Figure.Design a hydraulic accumulator of the type shown in Figure. The liquid volume in the accumulator should increase by 30in.3 when the pressure p increases by 1.5 lb/in.2. Determine suitable values for the plate area A and the spring constant k.

Q:Consider the liquid-level system treated in Example 7.4.10 and shownConsider the liquid-level system treated in Example 7.4.10 and shown in Figure 1 A.M. The pump curve and the line for the
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