Use MATLAB to plot the capacitor voltage in Problem 12. Data from Problem 12: Write the general form of the capacitor voltage for the electrical network shown in Figure P4.4. R = 10 k2 vit) = u(t) R2...

Solve for y(t) for the following system represented in state space, where u(t) is the unit step. Use the Laplace transform approach to solve the state equation. -3 1 01 X = |0 -6 1 x+1 u(t) 0 0 -5 y...

Figure P4.9 shows five step responses of an automatic voltage regulation system as one of the system parameters varies (Gozde, 2011). Assume for all five responses that they are those of a second...

Although the use of fractional calculus in control systems is not new, in the last decade there is increased interest in its use for several reasons. The most relevant are that fractional calculus...

If the tennis player serves the ball horizontally ( = 0), calculate its velocity v if the center of the ball clears the 0.9-m net by 150 mm. Also fi nd the distance s from the net to the point where...

A projectile is launched from point A with the initial conditions shown in the figure. Determine the slant distance s which locates the point B of impact. Calculate the time of flight t. vo = 120 m/s...

A projectile is launched from point A with an initial speed v 0 = 100 ft/sec. Determine the minimum value of the launch angle for which the projectile will land at point B. vo = 100 ft/sec A/a 80' ...

An earth satellite which moves in the elliptical equatorial orbit shown has a velocity v in space of 17 970 km/h when it passes the end of the semi minor axis at A. The earth has an absolute surface...

As it passes the position shown, the particle P has a constant speed v = 100 m/s along the straight line shown. Determine the corresponding values of r, , r, and . y v = 100 m/s P 30 80 ml 9. 80 m...

Determine the steady-state angle if the constant force P is applied to the cart of mass M. The pendulum bob has mass m and the rigid bar of length L has negligible mass. Ignore all friction....

For a given horizontal force P, determine the normal reaction forces at A and B. The mass of the cylinder is m and that of the cart is M. Neglect all friction. m A 60 B 60 P M

The system of the previous problem is now placed on the 15 incline. What force P will cause the normal reaction force at B to be zero? m M A B 60 P 60 15

The drive system of the 350-ton tugboat causes an external thrust P = 7000 lb to be applied as indicated in the figure. If the tugboat pushes an 800-ton coal barge starting from rest, what is the...

The inexperienced driver of an all-wheel-drive car applies too much throttle as he attempts to accelerate from rest up the slippery 10-percent incline. The result is wheel spin at all four tires,...

The 300-Mg jet airliner has three engines, each of which produces a nearly constant thrust of 240 kN during the takeoff roll. Determine the length s of runway required if the takeoff speed is 220 km...

The 750,000-lb jetliner A has four engines, each of which produces a nearly constant thrust of 40,000 lb during the takeoff roll. A small commuter aircraft B taxis toward the end of the runway at a...

cesium-ion engine for deep-space propulsion is designed to produce a constant thrust of 2.5 N for long periods of time. If the engine is to propel a 70-Mg spacecraft on an interplanetary mission,...

A toy train has magnetic couplers whose maximum attractive force is 0.2 lb between adjacent cars. What is the maximum force P with which a child can pull the locomotive and not break the train apart...

A worker develops a tension T in the cable as he attempts to move the 50-kg cart up the 20 incline. Determine the resulting acceleration of the cart if (a) T = 150 N and (b) T = 200 N. Neglect all...

The wheeled cart of Prob. 3 /19 is now replaced with a 50-kg sliding wooden crate. The coefficients of static and kinetic friction are given in the figure. Determine the acceleration of the crate if...

The 5-oz pinewood-derby car is released from rest at the starting line A and crosses the finish line C 2.75 sec later. The transition at B is small and smooth. Assume that the net retarding force is...

The coefficient of static friction between the flat bed of the truck and the crate it carries is 0.30. Determine the minimum stopping distance s which the truck can have from a speed of 70 km / h...

If the truck of Prob. 3/24 comes to a stop from an initial forward speed of 70 km / h in a distance of 50 m with uniform deceleration, determine whether or not the crate strikes the wall at the...

Determine the vertical acceleration of the 60-lb cylinder for each of the two cases. Neglect friction and the mass of the pulleys. 60 lb 40 lb 60 lb 40 lb (a) (b)

The rack has a mass m = 50 kg. What moment M must be exerted on the gear wheel by the motor in order to accelerate the rack up the 60 incline at a rate a = g/4? The fixed motor which drives the gear...

A jet airplane with a mass of 5 Mg has a touchdown speed of 300 km / h, at which instant the braking parachute is deployed and the power shut off. If the total drag on the aircraft varies with...

During its final approach to the runway, the aircraft speed is reduced from 300 km / h at A to 200 km / h at B. Determine the net external aerodynamic force R which acts on the 200-Mg aircraft during...

Determine the range of applied force P over which the block of mass m 2 will not slip on the wedge-shaped block of mass m 1 . Neglect friction associated with the wheels of the tapered block. m2 Hs =...

A heavy chain with a mass per unit length is pulled by the constant force P along a horizontal surface consisting of a smooth section and a rough section. The chain is initially at rest on the rough...

The sliders A and B are connected by a light rigid bar of length l = 0.5 m and move with negligible friction in the slots, both of which lie in a horizontal plane. For the position where x A = 0.4 m,...

The sliders A and B are connected by a light rigid bar and move with negligible friction in the slots, both of which lie in a horizontal plane. For the position shown, the velocity of A is 0.4 m /s...

The design of a lunar mission calls for a 1200-kg spacecraft to lift off from the surface of the moon and travel in a straight line from point A and pass point B. If the spacecraft motor has a...

Two iron spheres, each of which is 100 mm in diameter, are released from rest with a center-to-center separation of 1 m. Assume an environment in space with no forces other than the force of mutual...

The small 2-kg block A slides down the curved path and passes the lowest point B with a speed of 4 m /s. If the radius of curvature of the path at B is 1.5 m, determine the normal force N exerted on...

A spring-loaded device imparts an initial vertical velocity of 50 m/s to a 0.15-kg ball. The drag force on the ball is F D = 0.002v 2 , where F D is in newtons when the speed v is in meters per...

The system is released from rest in the configuration shown at time t = 0. Determine the time t when the block of mass m 1 contacts the lower stop of the body of mass m 2 . Also, determine the...

The system of Prob. 3/43 is reconsidered here, only now the interface between the two bodies is not smooth. Use the values s = 0.10 and k = 0.08 between the two bodies. Determine the time t when m...

The rod of the fixed hydraulic cylinder is moving to the left with a speed of 100 mm /s, and this speed is momentarily increasing at a rate of 400 mm/s each second at the instant when s A = 425 mm....

The particle of mass m is attached to the light rigid rod, and the assembly rotates about a horizontal axis through O with a constant angular velocity = . Determine the tension T in the rod as a...

If the 180-lb ski-jumper attains a speed of 80 ft /sec as he approaches the takeoff position, calculate the magnitude N of the normal force exerted by the snow on his skis just before he reaches A....

The 4-oz slider has a speed v = 3 ft /sec as it passes point A of the smooth guide, which lies in a horizontal plane. Determine the magnitude R of the force which the guide exerts on the slider (a)...

In the design of a space station to operate outside the earths gravitational field, it is desired to give the structure a rotational speed N which will simulate the effect of the earths gravity for...

During a brake test, the rear-engine car is stopped from an initial speed of 100 km/h in a distance of 50 m. If it is known that all four wheels contribute equally to the braking force, determine the...

The hollow tube is pivoted about a horizontal axis through point O and is made to rotate in the vertical plane with a constant counterclockwise angular velocity = 3 rad /sec. If a 0.2-lb particle is...

A Formula-1 car encounters a hump which has a circular shape with smooth transitions at both ends. (a) What speed vB will cause the car to lose contact with the road at the topmost point B? (b) For a...

The small spheres are free to move on the inner surface of the rotating spherical chambers shown in section with radius R = 200 mm. If the spheres reach a steady-state angular position = 45,...

A child twirls a small 50-g ball attached to the end of a 1-m string so that the ball traces a circle in a vertical plane as shown. What is the minimum speed v which the ball must have when in...

A small object A is held against the vertical side of the rotating cylindrical container of radius r by centrifugal action. If the coefficient of static friction between the object and the container...

The flatbed truck carries a large section of circular pipe secured only by the two fixed blocks A and B of height h. The truck is in a left turn of radius . Determine the maximum speed for which the...

A 180-lb snowboarder has speed v = 15 ft/sec when in the position shown on the halfpipe. Determine the normal force on his snowboard and the magnitude of his total acceleration at the instant...

Calculate the necessary rotational speed N for the aerial ride in an amusement park in order that the arms of the gondolas will assume an angle = 60 with the vertical. Neglect the mass of the arms...

Repeat the previous problem, only now the slotted arm is rotating with angular velocity = 3 rad /s, and this rate is increasing at 5 rad /s 2 .

The configuration of Prob. 3/70 is now modified as shown in the figure. Use all the data of Prob. 3/70 and determine the forces applied to the slider B by both arm OA and the sides of the slot....

Determine the altitude h (in kilometers) above the surface of the earth at which a satellite in a circular orbit has the same period, 23.9344 h, as the earths absolute rotation. If such an orbit lies...

The rotating drum of a clothes dryer is shown in the figure. Determine the angular velocity of the drum which results in loss of contact between the clothes and the drum at = 50. Assume that the...

The spacecraft P is in the elliptical orbit shown. At the instant represented, its speed is v = 13,244 ft /sec. Determine the corresponding values of r, , r, and . Use g = 32.23 ft /sec 2 as the...

At the instant under consideration, the cable attached to the cart of mass m 1 is tangent to the circular path of the cart. If the upward speed of the cylinder of mass m 2 is v 2 = 1.2 m/s, determine...

A small coin is placed on the horizontal surface of the rotating disk. If the disk starts from rest and is given a constant angular acceleration = , determine an expression for the number of...

The 2-kg collar is at rest in position A when the constant force P is applied as shown. Determine the speed of the collar as it passes position B if (a) P = 25 N (b) P = 40 N. The curved rod lies in...

The 6-kg cylinder is released from rest in the position shown and falls on the spring, which has been initially precompressed 50 mm by the light strap and restraining wires. If the stiffness of the...

Calculate the maximum velocity of slider B if the system is released from rest with x = y. Motion is in the vertical plane. Assume that friction is negligible. The sliders have equal masses, and the...

The 15 200-kg lunar lander is descending onto the moons surface with a velocity of 2 m/s when its retro-engine is fired. If the engine produces a thrust T for 4 s which varies with time as shown and...

A bead with a mass of 0.25 kg is released from rest at A and slides down and around the fixed smooth wire. Determine the force N between the wire and the bead as it passes point B. A 0.6 m B 45 0.15 m

The 80-lb boy has taken a running jump from the upper surface and lands on his 10-lb skateboard with a velocity of 16 ft/sec in the plane of the figure as shown. If his impact with the skateboard has...

The 6-kg sphere and 4-kg block (shown in section) are secured to the arm of negligible mass which rotates in the vertical plane about a horizontal axis at O. The 2-kg plug is released from rest at A...

The 0.4-lb ball and its supporting cord are revolving about the vertical axis on the fixed smooth conical surface with an angular velocity of 4 rad /sec. The ball is held in the position b = 14 in....

The figure shows a centrifugal clutch consisting in part of a rotating spider A which carries four plungers B. As the spider is made to rotate about its center with a speed , the plungers move...

The small car, which has a mass of 20 kg, rolls freely on the horizontal track and carries the 5-kg sphere mounted on the light rotating rod with r = 0.4 m. A geared motor drive maintains a constant...

The carriage of mass 2m is free to roll along the horizontal rails and carries the two spheres, each of mass m, mounted on rods of length l and negligible mass. The shaft to which the rods are...

Reduce the system shown in Figure P5.4 to a single transfer function, T(s) = C(s)/R(s). G3 R(s) C(s) G1 G2 G4 FIGURE P5.4

The 300-kg and 400-kg mine cars are rolling in opposite directions along the horizontal track with the respective speeds of 0.6 m/s and 0.3 m/s. Upon impact the cars become coupled together. Just...

A jet-engine noise suppressor consists of a movable duct which is secured directly behind the jet exhaust by cable A and deflects the blast directly upward. During a ground test, the engine sucks in...

A 2-oz bullet is fired horizontally with a velocity v = 1000 ft/sec into the slender bar of a 3-lb pendulum initially at rest. If the bullet embeds itself in the bar, compute the resulting angular...

Exercise 4.2 gives the probability distribution for the number Y of homes with high dust mite levels. a. Find E(Y). Give a meaningful interpretation of the result. b. Find s. c. Find the exact...

Use MATLABs Simulink to obtain the step response of a system, under the following conditions: a. The system is linear and driven by an amplifier whose gain is 10. b. An amplifier whose gain is 10...

Given the system below, draw a signal-flow graph and represent the system in state space in the following forms: a. Phase-variable form b. Cascade form 200 G(s) (s + 10)(s + 20)(s+ 30)

For the system shown in Figure P5.15, find K and to yield a settling time of 0.12 second and a 20% overshoot. R(s) E(s) K C(s) s(s + a) FIGURE P5.15

Figure P5.53 shows the block diagram of a possible cascade control scheme for an HEV driven by a dc motor (Preitl, 2007). Let the speed controller G SC (s) = 100 + 40/s, the torque controller and...

Given the HIV system of Problem 84 in Chapter 4 and repeated here for convenience (Craig, 2004): Express the system in the following forms: a. Phase-variable form b. Controller canonical form c....

Effective maintenance of equipment depends on the ability to accurately forecast the demand for spare parts. The Journal of Quality in Maintenance Engineering (Vol. 18, 2012) developed a statistical...

Let X and Y be two continuous random variables with joint probability density a. Find the value of c. b. Find f 1 (x). c. Find f 2 (y). d. Find f 1 (x y). e. Find f 2 (x y). f. Find P (X 1 and Y ...

The Scotch-yoke mechanism of Prob. 5/34 is modified as shown in the figure. For given values of , , r, , d, and , determine the velocity and acceleration of point P of the shaft. at P d- B

The space shuttle, together with its central fuel tank and two booster rockets, has a total mass of 2.04(10 6 ) kg at liftoff. Each of the two booster rockets produces a thrust of 11.80(10 6 ) N, and...

Motion of the wheel as it rolls up the fixed rack on its geared hub is controlled through the peripheral cable by the driving wheel D, which turns counterclockwise at the constant rate 0 = 4 rad/s...

The Geneva wheel is a mechanism for producing intermittent rotation. Pin P in the integral unit of wheel A and locking plate B engages the radial slots in wheel C, thus turning wheel C one-fourth of...

The shaft of the wheel unit rolls without slipping on the fixed horizontal surface, and point O has a velocity of 3 ft /sec to the right. By the method of this article, determine the velocities of...

The 64.4-lb solid circular disk is initially at rest on the horizontal surface when a 3-lb force P, constant in magnitude and direction, is applied to the cord wrapped securely around its periphery....

The uniform bar of mass m is supported by the smooth pin at O and is connected to the cylinder of mass m 1 by the light cable which passes over the light pulley at C. If the system is released from...

The circular disk of radius r rotates about a fixed axis through point O with the angular properties indicated in the figure. Determine the instantaneous velocity and acceleration of point A. Take...

The cable drum has a mass of 800 kg with radius of gyration of 480 mm about its center O and is mounted in bearings on the 1200-kg carriage. The carriage is initially moving to the left with a speed...

When a 3-kg collar is placed upon the pan which is attached to the spring of unknown constant, the additional static deflection of the pan is observed to be 42 mm. Determine the spring constant k in...

The 4-oz slider oscillates in the fixed slot under the action of the three springs, each of stiffness k = 0.5 lb/in. If the initial conditions at time t = 0 are x0 = 0.1 in. and x0 = 0.5 in./sec,...

The system shown is released from rest from an initial position x 0 . Determine the overshoot displacement x 1 . Assume translational motion in the x-direction. k = 108 N/m c 18 N.s/m m = 3 kg t X1

Find analytical expressions for the magnitude and phase response for each G(s) below. a. b. c. 1 G(s) = s(s +2)(s+ 4)

Consider the unity feedback system shown in Figure P9.1 with a. Design a compensator that will yield K p = 20 without appreciably changing the dominant pole location that yields a 10% overshoot for...

Briefly describe the design procedure for a controller.

Design a PI controller to drive the step response error to zero for the unity feedback system shown in Figure P9.1, where The system operates with a damping ratio of 0.6. Compare the specifications...

Determine the value of the viscous damping coefficient c for which the system is critically damped. The cylinder mass is m = 2 kg and the spring constant is k = 150 N/m. Neglect the mass and friction...

The end rollers of the bent bar ADB are confined to the slots shown. If v B = 0.3 m/s, determine the velocity of roller A and the angular velocity of the bar. 90 mm 30 B D 90 mm UB B = 15

The sector and attached wheels are released from rest in the position shown in the vertical plane. Each wheel is a solid circular disk weighing 12 lb and rolls on the fixed circular path without...