10.2.1 - Underdamped Case (ζ<1)
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Practice Questions
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Define the damping ratio.
💡 Hint: Think about how quickly the system stops moving.
What is the formula for the damped natural frequency?
💡 Hint: Consider the relationship between the natural frequency and damping.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is characterized by a damping ratio less than 1?
💡 Hint: Remember what happens when the damping ratio is low.
True or False: The impulse response function can predict behavior for all systems including nonlinear systems.
💡 Hint: Think about the properties of linear versus nonlinear systems.
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Challenge Problems
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Calculate the damped natural frequency for a system with a natural frequency of 5 Hz and a damping ratio of 0.3.
💡 Hint: Use the formula ω_d = ω_n √(1 - ζ²).
Explain how increasing the damping ratio would affect the oscillations of a structure during an earthquake.
💡 Hint: Consider the balance between oscillation and damping energy.
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