Consider the double pendulum pictured above, where both rods have negligible mass. Let 21, 3₁ and 2, 32 refer to the positions of the upper and lower mass respectively. 5. 6. 7. 8. 9. Write the equations of motion. Rewrite the equations of motion in the small-angle limit, using wo = √g/l. Assume the solutions to the equations above are of the form 0₁ = Aelwt, Beit 0₂: = Use the equations of motion (in the small-angle limit) to write corresponding equations in terms of w. Solve for w. There should be two solutions to the quadratic equation, w+ and w. For each value of w, solve for A and B, i.e. find A+, B+ and A-, B_.

Consider the double pendulum pictured above, where both rods have negligible mass. Let 21, 3₁ and 2, 32 refer to the positions of the upper and lower mass respectively. 5. 6. 7. 8. 9. Write the equations of motion. Rewrite the equations of motion in the small-angle limit, using wo = √g/l. Assume the solutions to the equations above are of the form 0₁ = Aelwt, Beit 0₂: = Use the equations of motion (in the small-angle limit) to write corresponding equations in terms of w. Solve for w. There should be two solutions to the quadratic equation, w+ and w. For each value of w, solve for A and B, i.e. find A+, B+ and A-, B_.

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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Forced undamped vibrations

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Question

I need some help with this classical mechanics question.

5.
6.
7.
2
8.
9.
m
е
m
Consider the double pendulum pictured above, where both rods have negligible mass. Let 2₁,3₁
and 22,32 refer to the positions of the upper and lower mass respectively.
0₂
Write the equations of motion.
Rewrite the equations of motion in the small-angle limit, using wo = √√√g/l.
Assume the solutions to the equations above are of the form
0₁ = Aelwt
0₂= Beit
Use the equations of motion (in the small-angle limit) to write corresponding equations in
terms of w.
Solve for w. There should be two solutions to the quadratic equation, w+ and w_.
For each value of w, solve for A and B, i.e. find A+, B+ and A-, B_.

Branch of science that deals with the stationary and moving bodies under the influence of forces.

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Step 4: Equation of motion in terms of ω

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