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Question 2 (40 Points) Consider the following double pendulum-like system with links ₁ and 12. The angles 0 and & could have angular velocities ėêk and êk, respectively, where ②k is a unit vector that points out of the page and is perpendicular to x and y. They could also have angular accelerations Ök and êk. The angle is defined relative to the angle 0. The link 12 is a spring and can extend or compress at a rate of 12. It can also have a rate of extension or compression Ï2. li y êr1 êe 12 χ 3 еф er2 ده لج 1) Express the velocity of the mass in terms of the unit vectors ê0, êr1, êø, and êr2, and any extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 2) Express the acceleration of the mass in terms of the unit vectors ê¤, ê×1, êp, and êÃ2, and any extension/contraction of the links (e.g.,. İ; and Ï¿) (12 Points) 3) Express the velocity of the mass in terms of unit vectors î and ĵ that point in the x and y directions, respectively. Also include the appropriate, extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 4) Suppose you wanted the system to move as a rigid body about the base pivot point O. What conditions would you have to apply to the velocity terms that you found in part 1? (4 points)

Question 2 (40 Points) Consider the following double pendulum-like system with links ₁ and 12. The angles 0 and & could have angular velocities ėêk and êk, respectively, where ②k is a unit vector that points out of the page and is perpendicular to x and y. They could also have angular accelerations Ök and êk. The angle is defined relative to the angle 0. The link 12 is a spring and can extend or compress at a rate of 12. It can also have a rate of extension or compression Ï2. li y êr1 êe 12 χ 3 еф er2 ده لج 1) Express the velocity of the mass in terms of the unit vectors ê0, êr1, êø, and êr2, and any extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 2) Express the acceleration of the mass in terms of the unit vectors ê¤, ê×1, êp, and êÃ2, and any extension/contraction of the links (e.g.,. İ; and Ï¿) (12 Points) 3) Express the velocity of the mass in terms of unit vectors î and ĵ that point in the x and y directions, respectively. Also include the appropriate, extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 4) Suppose you wanted the system to move as a rigid body about the base pivot point O. What conditions would you have to apply to the velocity terms that you found in part 1? (4 points)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question 2 (40 Points) Consider the following double pendulum-like system with links ₁ and 12. The angles 0 and & could have angular velocities ėêk and êk, respectively, where ②k is a unit vector that points out of the page and is perpendicular to x and y. They could also have angular accelerations Ök and êk. The angle is defined relative to the angle 0. The link 12 is a spring and can extend or compress at a rate of 12. It can also have a rate of extension or compression Ï2. li y êr1 êe 12 χ 3 еф er2 ده لج 1) Express the velocity of the mass in terms of the unit vectors ê0, êr1, êø, and êr2, and any extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 2) Express the acceleration of the mass in terms of the unit vectors ê¤, ê×1, êp, and êÃ2, and any extension/contraction of the links (e.g.,. İ; and Ï¿) (12 Points) 3) Express the velocity of the mass in terms of unit vectors î and ĵ that point in the x and y directions, respectively. Also include the appropriate, extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 4) Suppose you wanted the system to move as a rigid body about the base pivot point O. What conditions would you have to apply to the velocity terms that you found in part 1? (4 points)
Transcribed Image Text:Question 2 (40 Points) Consider the following double pendulum-like system with links ₁ and 12. The angles 0 and & could have angular velocities ėêk and êk, respectively, where ②k is a unit vector that points out of the page and is perpendicular to x and y. They could also have angular accelerations Ök and êk. The angle is defined relative to the angle 0. The link 12 is a spring and can extend or compress at a rate of 12. It can also have a rate of extension or compression Ï2. li y êr1 êe 12 χ 3 еф er2 ده لج 1) Express the velocity of the mass in terms of the unit vectors ê0, êr1, êø, and êr2, and any extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 2) Express the acceleration of the mass in terms of the unit vectors ê¤, ê×1, êp, and êÃ2, and any extension/contraction of the links (e.g.,. İ; and Ï¿) (12 Points) 3) Express the velocity of the mass in terms of unit vectors î and ĵ that point in the x and y directions, respectively. Also include the appropriate, extension/contraction of the links (e.g.,. i; and Ï¿) (12 Points) 4) Suppose you wanted the system to move as a rigid body about the base pivot point O. What conditions would you have to apply to the velocity terms that you found in part 1? (4 points)
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