Practice Numerical Solution of Free Vibration (Finite Difference Method) - 7.15 | 7. Free Vibration of Single Degree of Freedom (SDOF) System | Earthquake Engineering - Vol 1
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7.15 - Numerical Solution of Free Vibration (Finite Difference Method)

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the finite difference method?

💡 Hint: Think about how we might break up time into smaller sections.

Question 2

Easy

Why might we need to discretize time?

💡 Hint: Consider why continuous equations can be challenging.

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 finite difference method primarily address?

  • Analytical solutions of equations
  • Numerical solutions of dynamic problems
  • Geometric properties analysis

💡 Hint: Recall the primary uses of the method.

Question 2

True or False: The finite difference method can model continuous systems with variable properties more effectively than analytical methods.

  • True
  • False

💡 Hint: Think about the advantages over analytical methods.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Using the finite difference method, if a system has a natural frequency of 5 rad/s and initial displacements of x(0)=0 and x(1)=0.1, calculate the displacement at the next time step given a Δt of 0.1 seconds.

💡 Hint: Start by identifying your constants and then plug into the formula appropriately.

Question 2

Discuss the impact of increasing the time step size on the accuracy of results obtained from the finite difference method.

💡 Hint: Consider how a larger time step could skip details of the system's motion.

Challenge and get performance evaluation