Practice Equations of Motion - 16.3.2 | 16. Introduction to MDOF Systems | Earthquake Engineering - Vol 2
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Equations of Motion

16.3.2 - Equations of Motion

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does the mass matrix [M] represent?

💡 Hint: Think about what physical property the matrix relates to.

Question 2 Easy

What is the significance of external force vector {f(t)}?

💡 Hint: Remember how these forces influence movement.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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)}

💡 Hint: Focus on the absence of the damping term.

Question 2

True or False: The damping matrix [C] is included only in damped MDOF systems.

True
False

💡 Hint: Think about the effects of damping.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

💡 Hint: Use the definition of MDOF systems and substitute the matrices.

Challenge 2 Hard

An MDOF system has an undamped response. How would you adjust the equation to account for damping, and what implications might that have?

💡 Hint: Consider how energy dissipation modifies overall response.

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