10.3 - Derivation of Duhamel’s Integral
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Practice Questions
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What does Duhamel's Integral allow us to calculate?
💡 Hint: Think about earthquake analysis.
Define impulse response function.
💡 Hint: What happens when a singular force hits the system?
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Interactive Quizzes
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What is the primary use of Duhamel's Integral?
💡 Hint: Think about its application in earthquake engineering.
True or False: Superposition applies only to nonlinear systems.
💡 Hint: Consider the definitions of linear versus nonlinear.
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Challenge Problems
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Given a linear system with mass m, damping coefficient c, and stiffness k, derive the Duhamel Integral expression for the system's response to a sinusoidal force F(t) = F₀ sin(ωt).
💡 Hint: Consider how the sine function influences the system's response over its period.
Assuming a damping ratio ζ < 1, explain how the impulse response changes compared to critically damped and overdamped systems.
💡 Hint: Think about the differences in energy dissipation and speed of return to equilibrium.
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