- #1
Setareh7796
- 9
- 0
- Homework Statement
- I am not sure where I am going wrong because I am not getting the right answer.
- Relevant Equations
- mz̈ + kz = 0
Finding equations of motion of multi degree freedom system
- Thread starter Setareh7796
- Start date
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The discussion focuses on deriving equations of motion for a multi-degree freedom system, specifically addressing matrix formulations. The arithmetic for the first line of the matrix is confirmed to be correct, resulting in a total of \(\frac{11}{3}k\). However, issues arise in the second line, where terms are not combined properly, leading to confusion in matrix entries. The correct combination of terms should yield \(\frac{22}{15}k\). Overall, clarity in combining like terms is essential for accurate matrix representation in the equations of motion.
- #2
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\frac{2k^2}{2k+k} = \frac{2}{3}k
in your first line of your second matrix:
3k+ \frac{2}{3}k = \frac{9}{3}k + \frac{2}{3}k = \frac{11}{3}k
so you're good there once you do the arithmetic.
second line... hmmm.
-\frac{2k^2}{2k+k}x_1 +\left(\frac{2k^2}{2k+k} + \frac{4k^2}{4k+k} \right)x_2
\frac{2}{3}k + \frac{4}{5}k = \frac{10+12}{15}k = \frac{22}{15}k
I see no problems except that you're not combining like terms but instead writing those terms as separate matrix entries.
in your first line of your second matrix:
3k+ \frac{2}{3}k = \frac{9}{3}k + \frac{2}{3}k = \frac{11}{3}k
so you're good there once you do the arithmetic.
second line... hmmm.
-\frac{2k^2}{2k+k}x_1 +\left(\frac{2k^2}{2k+k} + \frac{4k^2}{4k+k} \right)x_2
\frac{2}{3}k + \frac{4}{5}k = \frac{10+12}{15}k = \frac{22}{15}k
I see no problems except that you're not combining like terms but instead writing those terms as separate matrix entries.
TL;DR: This determine the support reactions at A & B
I tried calculate moment about a which is 2a(By + Bx + Ey + Ex +F) + a (Gy + Gx + Cy + Cx). But I don't think I'm correct, any help would be appreciated, this was a question on a final exam paper in my Mechanics course.
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