Practice Applications In Civil Engineering (3.4) - Second-Order Homogeneous Equations with Constant Coefficients

Practice: Applications in Civil Engineering

Lesson 3.4Second-Order Homogeneous Equations with Constant Coefficients

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9 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the form of the equation for free vibration of structures?
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Consider the components of mass, damping, and stiffness.
Question 2.
What happens to the equation when q(x) = 0 in beam deflection?
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Think about the implications of having no external load.
3Question 3.
What does the characteristic equation derive from?
- Homogeneous equation
- Non-homogeneous equation
- Both
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Consider the nature of the equation you start with.
4Question 4.
True or False: The damping ratio less than one indicates an overdamped system.
- True
- False
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Think about the definitions of damping ratios.
Question 5.
Derive the characteristic equation for a cantilever beam subjected to a point load at the free end and discuss the physical implications.
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Recall the steps you've learned for deriving equations.
Question 6.
Analyze the behavior of a damped vibrating structure when subjected to alternating loads and describe the resulting motion.
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Consider drawing a phase space to visualize the oscillations.

5 more questions in this section. Enroll free to practise them all.