18.1.3 - Analogy with Free Vibration
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Practice Questions
Test your understanding with targeted questions
What is the purpose of the inertial force in a mass-spring system?
💡 Hint: Think about Newton's second law.
What kind of equation describes the motion of a free vibrating system?
💡 Hint: Can you remember the standard form for these equations?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the relationship between mass and inertial force?
💡 Hint: Recall F=ma from Newton's second law.
True or False: The characteristic equation can help determine a system's natural frequency.
💡 Hint: Think about why frequencies are important in vibrational analysis.
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Challenge Problems
Push your limits with advanced challenges
Consider a mass-spring system with m1 = 2 kg, m2 = 3 kg, and spring constants k1 = 100 N/m and k2 = 200 N/m. Derive the equations of motion and identify the natural frequencies.
💡 Hint: Utilize the characteristic equation for finding frequencies.
Explore how the system reacts when applied forces are changed. How would you expect the behavior to differ with increased stiffness?
💡 Hint: Visualize the difference in a stiffer vs. looser spring.
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