Given the system represented in state space as follows: convert the system to one where the new state vector, z, is -1 -7 6 -5 -8 4 8 x+ -7r 4 7 -8 y = [-9 -9 -8] x

For the system shown in Figure P7.3, what steady-state error can be expected for the following test inputs: 10u(t); 10tu(t); 10t 2 u(t). R(s) + 3 C(s) s+4 2 6s FIGURE P7.3

A drive system with an elastically coupled load was presented in Problem 71, Chapter 4. The mechanical part of this drive (Thomsen, 2011) was reduced to a two-inertia model. Using slightly different...

Statistical software packages, such as SAS and MINITAB, are capable of generating random numbers from a uniform distribution. For example, the SAS function RANUNI uses a prime modulus 2 31 1...

The rod OB slides through the collar pivoted to the rotating link at A. If CA has an angular velocity = 3 rad/s for an interval of motion, calculate the angular velocity of OB when = 45. CA = 200...

An inverted pendulum, mounted on a motor-driven cart was presented in Chapter 3, Problem 30. The systems state-space model was linearized around a stationary point, x 0 = 0, corresponding to the...

Motion of the roller A against its restraining spring is controlled by the downward motion of the plunger E. For an interval of motion the velocity of E is v = 0.2 m/s. Determine the velocity of A...

The uniform steel I-beam has a mass of 300 kg and is supported in the vertical plane as shown. Calculate the force R supported by the pin at O for the condition immediately after the support at B is...

The 1800-kg rear-wheel-drive car accelerates forward at a rate of g/2. If the modulus of each of the rear and front springs is 35 kN/m, estimate the resulting momentary nose-up pitch angle . (This...

A linear harmonic oscillator having a mass of 1.10 kg is set into motion with viscous damping. If the frequency is 10 Hz and if two successive amplitudes a full cycle apart are measured to be 4.65 mm...

For each of the root loci shown in Figure P8.1, tell whether or not the sketch can be a root locus. If the sketch cannot be a root locus, explain why. Give all reasons. jo ja ja ja s-plane s-plane...

In order to determine controllability mathematically, the controllability matrix is formed, and its rank evaluated. What is the final step in determining controllability if the controllability matrix...

The uniform rod of mass m is freely pivoted about point O. Assume small oscillations and determine an expression for the damping ratio . For what value c cr of the damping coefficient c will the...

Refer to the Behavioral Neuroscience (Feb. 2004) study of the drug scopolamines effects on memory for word-pair associates, Exercise 14.13. Recall that a completely randomized design with three...

Calculate the bending moment M in the shaft at O for the rotating assembly of Prob. 7/144 as it starts from rest with an initial angular acceleration of 200 rad/s 2 . N - 150 mm 75 mm 150 mm 75 mm...

Refer to the Evolutionary Ecology Research (July 2003) study of the New Zealand bird population prior to European contact, Exercise 1.12. Two quantitative variables measured for each of The 116 bird...

Glycolysis is a feedback process through which living cells use glucose to generate adenosine triphosphate (ATP), necessary for cell operations. A linearized glycolysis model (Chandra, 2011) is given...

The body composed of slender rods of mass p per unit length is lying motionless on the smooth horizontal surface when a linear impluse P dt is applied as shown. Determine the velocity v B of corner B...

A marine biologist was hired by the EPA to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on the marine life in the area....

Corporate sustainability refers to business practices designed around social and environmental considerations (e.g., going green and energy conservation). Business and Society (March 2011) published...

Refer to the Behavioral Neuroscience (Feb. 2004) study of the drug scopolamines effects on memory for word-pair associates, Exercise 14.13. Recall that the researchers theorized that the mean number...

The one-dimensional monatomic harmonic crystal (Sect. 6.1.3) is in fact a particular case of the diatomic model described in Sect. 6.1.4, for which the two atoms are identical. To prove this, show...

Refer to the Journal of Food Engineering (Sep., 2013) study of the characteristics of sweet potato chips fried at different temperatures, Exercise 7.75. Recall that a sample of 6 sweet potato slices...

Consider a single jet of water striking the buckets of the impulse wheel as shown. Assume ideal conditions for power generation [V bucket = (1/2)V j and the jet is turned through 180 of arc]. With...

A jet of water (60F) is discharging at a constant rate of 2.0 cfs from the upper tank. If the jet diameter at section 1 is 4 in., what forces will be measured by scales A and B? Assume the empty tank...

The discharge in the siphon is 2.5 cfs, D = 7 in., L 1 = 4 ft , and L 2 = 5 ft. Determine the head loss between the reservoir surface and point C. Determine the pressure at point B if three quarters...

Liquid benzene at 25C and 1.2 bar is converted to vapor at 200C and 5 bar in a twostep steady-flow process: compression by a pump to 5 bar, followed by vaporization in a counterflow heat exchanger....

The following empirical two-parameter expression has been proposed for correlation of excess properties of symmetrical liquid mixtures: Here, quantities A and B are parameters that depend at most on...

If V BR2 is 6.4 V, determine the range for V BR1 using Eq. (17.1). Eq. (17.1) VBR, = VBR, + 0.1VBR,

For the network of Fig. 7.81 , determine: a. V GSQ and I DQ . b. V DS , V D , V G , and V S . 12 V 2.2 ka oss = 6 mA. Vp =-6 V Vase 1 MO. 1.6 kn 3 V FIG. 7.81

Determine V D and V GS for the fixed-bias configuration of Fig. 7.78 . 20 V 2,2 k2 VD Ipss = 5 mA Vp = -5 V 1 MN FIG. 7.78

For the network of Fig. 4.136 , determine: a. I B . b. I C . c. V CE . d. V C . Fig. 4.136 9.1 9+16 V '12 le + = 80 15 6-12V FIG. 4.136

The specific weight (wt./vol.) of brass is 520 lb/ft3. Determine its density (mass/vol.) in SI units. Use an appropriate prefix.

A specimen of an AISI-SAE type 416 stainless steel with a 0.505-in. diameter was machined to a 2.00-in.-gage length and the following data were collected: After fracture, the gage length was 2.20 in....

Determine the coordinate angle for F 2 and express each force acting on the bracket as a Cartesian vector. X N 45 60 F = 450 N 45. 30 F = 600 N -y

Determine the force in each cable needed to support the 500-lb cylinder. 3 ft 6 ft B -6 ft- D N 3 ft 5 ft C 6 ft 2 ft y

Determine the magnitude and coordinate direction angles of the resultant of the two forces acting at point A. X Fc= 400 N, 2m FE=350 N FB = 400 N 3 m E 2 m E 2 m B 3m

Three forces act on the ring. Determine the magnitude and coordinate direction angles of the resultant force. F = 500 N 30 X 60 F3 = 100 N 60 120 F = 400 N 45 y

The hold-down clamp exerts a compressive force of 400 N on the wood block at C. If the clamp is loosely bolted to the bench using two symmetrically placed bolts B, one of which is shown, determine...

Replace the loading acting on the beam by a single resultant force. Specify where the force acts, measured from B. 60 450 N |--2m--- -4 m- 300 N B -3m- 700 N 30 1500 Nm

Replace the loading acting on the frame by an equivalent resultant force and couple moment acting at point B. 80 lb + -3 ft- B -3 ft- 75 lb 60 lb + -3 ft- -3 ft- 2 ft + 40 lb A 4 ft

The clamp has a rated load capacity of 1500 lb. Determine the compressive force this creates along segment AB of the screw and the magnitude of force exerted at pin C. The screw is pin connected at...

Determine the reactions at pins A and B of the frame needed to support the 200-lb load. The pulley at C has a radius of 0.5 ft. The pulley at D has a radius of 0.25 ft. 4 ft 60% 30 30 3 ft B

Determine the horizontal and vertical components of force which pin C exerts on member ABC. The 600-N force is applied to the pin. 3 m 1.5 m -2m- E A F D B -2 m 300 N C 600 N

Determine the horizontal and vertical components of force acting at the pins A, B, and C of the frame. 4 ft 45 4 ft 100 lb 4 ft 100 lb 8 ft 30%

Determine the horizontal and vertical components of force that pins A and B exert on the frame. 4 m A -3 m- B C 2 kN/m

Determine the force required to hold the 50-kg mass in equilibrium. B C A B P 191

Determine the force in each member of the space truss and state if the members are in tension or compression. The The truss is supported by ball-and-socket joints at A, B, and E. Set F = {800j} N. 5...

Determine the components of reaction E. A E -1.5 m- 4 kN/m D -1.5 m- Prob. F6-23 B 2m C 5 kN

Determine the normal force that the 100-lb plate A exerts on the 30-lb plate B. -1 ft- A B -4 ft- Prob. F6-17 +1 ft-

If a 100-N force is applied to the handles of the pliers, determine the clamping force exerted on the smooth pipe B and the magnitude of the resultant force that one of the members exerts on pin A....

Determine the force P needed to hold the 60-lb weight in equilibrium. P 401 Prob. F6-13

Determine the force in members DC, HI, and JI of the truss and state if the members are in tension or compression. Suggestion: Use the sections shown. G T 6 ft 6 ft 12 ft ----|-6 ft-|-6 ft-|-- F -9...

Determine the force in members GF, GD, and CD of the truss and state if the members are in tension or compression. 1 m 2m A H B -2m-2m- 10 kN G C -2 m- D -2 m- 25 kN 15 kN

Determine the force in members EF, CF, and BC of the truss and state if the members are in tension or compression. G 30 6 ft B 300 lb F -6 ft- 300 lb E 30 6 ft

Determine the force in members KJ, KD, and CD of the Pratt truss and state if the members are in tension or compression. 3 m K B C D E H F -2 m--2 m--2 m--2 m--2 m--2 m- 20 KN 30 kN 40 kN G

Determine the force in each member of the truss. State if the members are in tension or compression. 600 16 450 lb YE A -3 ft- D B 30 -3 ft

Determine the greatest load P that can be applied to the truss so that none of the members are subjected to a force exceeding either 2 kN in tension or 1.5 kN in compression. A C 60 60 -3 m- Prob....

Determine the force in each member of the truss and state if the members are in tension or compression. Set P 1 = 200 lb, P 2 = 500 lb. 4 ft A -3 ft- B P - P -4 ft-

Determine the moment of each of the three forces about point A. F=250 N 30% A -2 m- -3 m B F = 300 N 60 4'm 5 F3 = 500 N

An antenna located at the origin has a far-zone electric field as (a) Obtain the corresponding H s field. (b) Determine the power radiated. (c) What fraction of the total power is radiated in the...

Determine the radius of gyration k y of the parabolic area. 160 mm y -y=0.1(1600-x) 40 mm X

Determine the moment of inertia I y of the shaded area about the y axis. 150 mm 150 mm O -100 mm-+-1 |- 100 mm-|-150 mm - 75 mm X

Round off the following numbers to three significant figures: (a) 3.45555 m, (b) 45.556 s, (c) 5555 N, (d) 4525 kg.

Determine the shear and moment as a function of .x, where 0 x < 3m and 3m < x 6m, and then draw the shear and moment diagrams. A 12 kN.m -3 m- 4 kN C 3 m- B

The bent rod is supported at A, B, and C by smooth journal bearings. Compute the x, y, z components of reaction at the bearings if the rod is subjected to forces F 1 = 300 lb and F 2 = 250 lb. F 1...

Determine the weight of the wedge which is formed by rotating a right triangle of base 6 in. and height 3 in. through an angle of 30. The specific weight of the material is = 0.22 lb/in 3 . 6 in. 30...

The load can be supported by two boys when the cord is suspended over the pipe (a half-turn). If each boy can pull with a force of 125 lb, determine the maximum weight of the load. Can one boy...

The 50-lb cylinder is attached to a cord which passes over the fixed drum. If the coefficient of static friction at the drum is s = 0.3, determine the maximum force P that can be applied to the...

Determine the minimum tension in the rope at points A and B which is necessary to maintain equilibrium. The coefficient of static friction between the rope and the fixed post D is s = 0.3. The rope...

Determine the force P that must be applied to the handle of the lever so that the wheel is on the verge of turning if M = 300 N m. The coefficient of static friction between the belt and the wheel...

The hand clamp is constructed using a square-threaded screw having a mean diameter of 36 mm, a lead of 4 mm, and a coefficient of static friction at the screw ofThe hand clamp is constructed using a...

A cone is attached to the hemisphere. If both pieces have the same density, determine the height h of the cone if the configuration is to be in neutral equilibrium. 3 ft h

Express the following in terms of r, , and : ar ar a 20

When the motorcyclist is at A, he increases his speed along the vertical circular path at the rate of v = (0.3t) ft/s, where t is in seconds and t = 0 at A. If he starts from rest at A, determine the...

a. Let (e1, e2, e2) be unit vectors of a right-handed, orthogonal coordinate system. Showthat the Levi-Civit`a symbol satisfies b. Prove that c. Prove that: d. In quantum mechanics, the Cartesian...

When t = 0, the train has a speed of 8 m/s, which is increasing at 0.5 m/s 2 . Determine the magnitude of the acceleration of the engine when it reaches point A, at t = 20 s. Here the radius of...

The pitching machine is adjusted so that the baseball is launched with a speed of v A = 30 m/s. If the ball strikes the ground at B, determine the two possible angles A at which it was launched. 1.2...

Molecules adsorbed on the surface of a solid crystal surface at low temperature typically arrange themselves into a periodic arrangement, e.g., one molecule lies at the center of each a a square of...

The parallel plates of a microchannel plate electron multiplier are segmented into conducting strips of width b so the potential can be fixed on the strips at staggered values. We model this using...

The truck has a mass of 1.25 Mg and a center of mass at G. Determine the greatest load it can move if (a) the truck has rear-wheel drive while the front wheels are free to roll, and (b) the truck has...

The disk rolls without slipping such that it has an angular acceleration of = 4 rad/s 2 and angular velocity of = 2 rad/s at the instant shown. Determine the acceleration of points A and B on the...

The center of the wheel is moving to the right with a speed of 2 ft/s. If no slipping occurs at the ground, A, determine the velocity of points B and C. 1.5 ft C A 30 2 ft/s B

The uniform slender rod has a mass of 5 kg. If the cord at A is cut, determine the reaction at the pin O, (a) When the rod is still in the horizontal position, and (b) When the rod swings to the...

A uniform plate has a weight of 50 lb. Link AB is subjected to a couple moment of M = 10 lb ft and has a clockwise angular velocity of 2 rad/s at the instant = 30. Determine the force developed in...

The door has a weight of 200 lb and a center of gravity at G. Determine the constant force F that must be applied to the door to push it open 12 ft to the right in 5 s, starting from rest. Also, find...

The slender rods have a weight of 3 lb/ft Determine the moment of inertia of the assembly about an axis perpendicular to the page and passing through point A. A -1.5 ft 1.5 ft 2 ft 1 ft

The uniform bar AB has a mass of 12 kg and is pin connected at A. If the support at B is remove ( = 90), determine the velocity of the 5-kg block C at the instant the bar rotates downward to = 150....

The 25-lb slender rod AB is attached to spring BC which has an unstretched length of 4 ft. If the rod is released from rest when = 30, determine its angular velocity at the instant = 90. C 4 ft k =...

A uniform ladder having a weight of 30 lb is released from rest when it is in the vertical position. If it is allowed to fall freely, determine the angle at which the bottom end A starts to lift off...

The 2-kg disk is thrown down onto the rough surface with the velocity and angular velocity shown. If there is no slipping, and the coefficient of restitution is e = 0.5, determine the velocity of the...

The global robot industry is growing rapidly A typical industrial robot has multiple degrees of freedom. A unity feedback position control system for a force-sensing joint has a loop transfer...

In the figure for Problem 13-35, pinion 2 is to be a right-hand helical gear having a helix angle of 30, a normal pressure angle of 20, 16 teeth, and a normal diametral pitch of 6 teeth/in. A motor...

An open office room holds 50 employees, each dissipating 430 kJ of energy as heat per hour. In addition, twenty 80 W light bulbs are all left on at all times. Calculate how many 6 kW air-conditioning...

Your company asks you, the process engineer, to estimate the rate at which energy is transferred as heat through a steam turbine casing. This turbine operates with an inlet pressure of 16 bar and an...

Consider a pistoncylinder assembly containing 0.12 kg of superheated steam at 700 kPa and 800 K (state 1). Energy is removed from the steam by heat transfer until a temperature of 400 K is reached...

Knowing that at the instant shown bar DE has an angular velocity of 20 rad/s clockwise and an angular acceleration of 5 rad/s 2 counterclockwise, determine in the position shown (a) The angular...

Carbon dioxide at P 1? and T 1 is contained inside a piston?cylinder. It undergoes polytropic compression according to the process equation PVn = constant.? a. Derive the formula for the energy...

Determine the force in each member of the truss and state whether it is in tension or compression. 2k A D 6 ft B 8 ft Prob. F3-4

Estimate the capital cost of a plant that produces 80,000 metric tons per year of caprolactam.