Introductory Mathematics for Engineering Applications
Introductory Mathematics for Engineering Applications
1st Edition
ISBN: 9781118141809
Author: Nathan Klingbeil
Publisher: WILEY
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Chapter 3, Problem 20P

Suppose that the two-link planar robot Shown in Fig. P3.18 is located in the first quadrant and is oriented in the elbow- down position. If the tip of the robot is located at the point P ( x , y ) = ( 10 , 5 ) , determine the values of θ 1 and θ 2 . Assume l 1 = 6 in, and l 2 = 8 in.

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2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.
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Chapter 3 Solutions

Introductory Mathematics for Engineering Applications

Ch. 3 - A one-link planar robot moves in the x -y plane as...Ch. 3 - A one-link planar robot mines in the x -y plane as...Ch. 3 - A one-link planar robot mines in the x -y plane as...Ch. 3 - Consider the one-link planar robot shown in Fig....Ch. 3 - Repeat problem P3-14 if l=10 in, and =150 rad =23...Ch. 3 - Consider again the one-link planar robot shown in...Ch. 3 - Repeat problem P3-16 if...Ch. 3 - Prob. 18PCh. 3 - Suppose that the two-link planar robot Shown in...Ch. 3 - Suppose that the two-link planar robot Shown in...Ch. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Consider a two-link planar robot oriented in the...Ch. 3 - An airplane travels at a heading of 600 northwest...Ch. 3 - A Large barge is crossing a river at a heading of...Ch. 3 - The impedance triangle of a resistor (R ) an...Ch. 3 - The impedance triangle of a resistor (R ) and a...Ch. 3 - The impedance triangle of a resistor (R ) an...Ch. 3 - The impedance triangle of a resistor (R ) and a...Ch. 3 - The phasor diagram of a series RL circuit is shown...Ch. 3 - The phasor diagram of a series RC circuit is shown...Ch. 3 - Prob. 36PCh. 3 - Consider the elevation between the two benchmarks...Ch. 3 - Repeat problem P3-37 if the distance L, between...Ch. 3 - Consider the elevation between the two benchmarks...Ch. 3 - Repeat problem P3-39 if the distance L between the...Ch. 3 - To find the height of a building, a surveyor...Ch. 3 - The gas boron trifluoride (BF3) has a trigonal...Ch. 3 - Prob. 43PCh. 3 - Repeat P3-43 if the force exerted by the...Ch. 3 - Consider the position of the toes of a person...Ch. 3 - In a motion capture study of a runner, one frame...
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