Practice Convolution Integral and General Force Response - 9.9 | 9. Impulse and Response to Unit Impulse | Earthquake Engineering - Vol 1
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9.9 - Convolution Integral and General Force Response

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the convolution integral used for in structural analysis?

💡 Hint: Think about how different inputs affect the output response.

Question 2

Easy

Define impulse response function.

💡 Hint: What happens when you apply an instantaneous force to a system?

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does the convolution integral signify?

  • It calculates only the impulse response
  • It combines responses to multiple forces
  • It measures the speed of a building

💡 Hint: Focus on the definition and purpose of convolution.

Question 2

True or False: The convolution integral can be used for non-linear systems.

  • True
  • False

💡 Hint: Remember the system types that allow the use of convolution.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

Question 2

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.

Challenge and get performance evaluation