13.15 - Civil Engineering Case Example: Convolution in Structural Dynamics
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Practice Questions
Test your understanding with targeted questions
What is the purpose of convolution in structural dynamics?
💡 Hint: Think about the interaction between two functions.
Give an example of ground motion function.
💡 Hint: What function describes oscillations due to seismic waves?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the convolution of f(t) and h(t) predict?
💡 Hint: Consider the output effect of seismic activity.
True or False: Convolution is solely used for time-series data analysis.
💡 Hint: Remember other fields where it's applied.
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Challenge Problems
Push your limits with advanced challenges
Given a building's impulse response function h(t) = \frac{1}{2} e^{-2t}, calculate the displacement response y(t) when subjected to f(t) = e^{-1.5t} \sin(3t).
💡 Hint: Remember to set limits of integration zero to t.
Discuss how changing the damping ratio in h(t) affects the building's response. Give a specific example.
💡 Hint: Think about energy dissipation in systems.
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