12.10 - Practical Examples
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Practice Questions
Test your understanding with targeted questions
What is the mathematical expression for a point load applied at the center of a simply supported beam?
💡 Hint: Think about where the load is positioned on the beam.
What type of function is the Dirac delta function?
💡 Hint: Consider its properties discussed earlier.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Dirac delta function model?
💡 Hint: Recall the key features of the Dirac delta function.
True or False: The impulse function can be expressed through the Dirac delta function in the time domain.
💡 Hint: Think about the properties of impulses in dynamics.
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Challenge Problems
Push your limits with advanced challenges
A simply supported beam of length 10 m is subject to a point load of 500 N at its center. Derive the deflection at the midpoint of the beam using the Dirac delta function and given E = 200 GPa, I = 5000 cm4.
💡 Hint: Break down the governing equation and apply integration techniques.
Analyze the response of a mass-spring-damper system under an impulse F(t) = 1000δ(t). Calculate its system response given m=1 kg, k=100 N/m, and b=10 N·s/m.
💡 Hint: Use the characteristic equation of the system and determine the form of the response due to this impulse.
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Reference links
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