- #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
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SUMMARY
The discussion focuses on deriving equations of motion for a multi-degree freedom system using matrix representation. Participants confirm the correctness of specific calculations involving stiffness coefficients, such as \(\frac{2k^2}{2k+k} = \frac{2}{3}k\) and \(\frac{11}{3}k\) in the context of matrix entries. The importance of combining like terms in matrix equations is emphasized, particularly in the second line of the matrix representation. Overall, the conversation highlights the critical arithmetic involved in formulating accurate equations of motion.
PREREQUISITES- Understanding of multi-degree freedom systems in dynamics
- Familiarity with matrix algebra and operations
- Knowledge of stiffness coefficients in mechanical systems
- Basic principles of equations of motion in physics
- Study the derivation of equations of motion for multi-degree freedom systems
- Learn about stiffness matrices and their applications in structural analysis
- Explore numerical methods for solving dynamic equations in mechanical systems
- Investigate software tools for simulating multi-degree freedom systems, such as MATLAB or Simulink
Mechanical engineers, students studying dynamics, and professionals involved in structural analysis and simulation of multi-degree freedom systems will benefit from this discussion.
- #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.
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