9.9 - Convolution Integral and General Force Response
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Practice Questions
Test your understanding with targeted questions
What is the convolution integral used for in structural analysis?
💡 Hint: Think about how different inputs affect the output response.
Define impulse response function.
💡 Hint: What happens when you apply an instantaneous force to a system?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the convolution integral signify?
💡 Hint: Focus on the definition and purpose of convolution.
True or False: The convolution integral can be used for non-linear systems.
💡 Hint: Remember the system types that allow the use of convolution.
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Challenge Problems
Push your limits with advanced challenges
Consider a simple SDOF system with an impulse response function defined as h(t) = e^(-ζω_nt)sin(ω_dt). If subjected to a constant force F(t)=F_0 for a time window from 0 to T, how would you compute the resultant displacement x(t)?
💡 Hint: Think about the shape of the impulse response and how it behaves with constants over time.
Given an external force F(t) = F_0 * cos(ωt) applied to an LTI system with a known impulse response h(t), derive the total response x(t) using the convolution integral.
💡 Hint: Remember the properties of convolution with sinusoidal inputs can lead to specific forms in the output.
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