Practice Equations Of Motion (16.3.2) - Introduction to MDOF Systems - Earthquake Engineering - Vol 2

Practice: Equations of Motion

Lesson 16.3.2Introduction to MDOF Systems

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9 questions

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6 sample questions

Question 1.
What does the mass matrix [M] represent?
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Think about what physical property the matrix relates to.
Question 2.
What is the significance of external force vector {f(t)}?
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Remember how these forces influence movement.
3Question 3.
What is the correct equation for an undamped MDOF system?
- [M]{u¨(t)} + [C]{u˙(t)} + [K]{u(t)} = {f(t)}
- [M]{u¨(t)} + [K]{u(t)} = {f(t)}
- [C]{u˙(t)} + [K]{u(t)} = {f(t)}
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Focus on the absence of the damping term.
4Question 4.
True or False: The damping matrix [C] is included only in damped MDOF systems.
- True
- False
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Think about the effects of damping.
Question 5.
Consider a two-degree-of-freedom MDOF system with mass matrix [M] = [2 0; 0 3] and stiffness matrix [K] = [4 -2; -2 3]. Derive the equation of motion for this system.
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Use the definition of MDOF systems and substitute the matrices.
Question 6.
An MDOF system has an undamped response. How would you adjust the equation to account for damping, and what implications might that have?
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Consider how energy dissipation modifies overall response.

5 more questions in this section. Enroll free to practise them all.