7.6 - Initial Conditions and System Response
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Practice Questions
Test your understanding with targeted questions
What is meant by initial displacement in an SDOF system?
💡 Hint: Think about the position relative to the resting state.
How does initial velocity differ from initial displacement?
💡 Hint: Consider it as the speed or rate of change of position.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the initial displacement x(0) represent in an SDOF system?
💡 Hint: Think about the starting point of oscillation.
True or False: Initial velocity has no effect on the amplitude of the vibration.
💡 Hint: Consider how speed at the start influences oscillation.
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Challenge Problems
Push your limits with advanced challenges
A block on a spring has an initial displacement of 2 m and is released with an initial velocity of 5 m/s. Find the equation for its motion and explain each component.
💡 Hint: Use the formula involving initial conditions to build the motion equation.
If the initial conditions of a system are altered such that the displacement is halved, but velocity doubles, derive the new equation of motion.
💡 Hint: Translate altered conditions into the motion equation format.
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