Practice Multi-Degree of Freedom (MDOF) Systems - 1.8 | 1. Theory of Vibrations | Earthquake Engineering - Vol 1
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Multi-Degree of Freedom (MDOF) Systems

1.8 - Multi-Degree of Freedom (MDOF) Systems

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What does MDOF stand for?

💡 Hint: Consider how it relates to the dimensions of motion.

Question 2 Easy

Define the mass matrix in the context of MDOF systems.

💡 Hint: It's related to how much mass affects motion.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the primary equation governing MDOF systems?

[M]{ẍ} + [C]{x˙} + [K]{x} = {F(t)}
[K]{x} + [M]{x} = 0
[C]{x} = {F(t)}

💡 Hint: Look for the equation combining all key system properties.

Question 2

True or False: Mode shapes represent how a system vibrates at its natural frequencies.

True
False

💡 Hint: Think about what happens during free vibrations.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

A three-story building is modeled as a 3-DOF system. Given the mass matrix [M] as diag(2000, 1500, 1000) kg and the stiffness matrix [K] as diag(5000, 4000, 3000) N/m, determine the estimation of natural frequencies.

💡 Hint: Remember to formulate the matrix to solve for characteristic polynomial.

Challenge 2 Hard

Analyze the impact of increasing damping in an MDOF system on its mode shapes and natural frequencies. What criteria will you consider?

💡 Hint: Consider how damping affects dynamic stability and frequency response.

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Reference links

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