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Governing Equations for Single Degree of Freedom Systems

Learn the governing equations (equations of motion) for SDOF systems by equivalent energy method and Newton's Second Law. Find equivalent mass and stiffness, solve with Free-Body Diagrams, and define damping constants. Practice examples and self-solving during class.

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Governing Equations for Single Degree of Freedom Systems

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  1. WEEK-2: Governing equation of SDOF systems Assoc. Prof. Dr. Abdullah Seçgin

  2. Governing equation (Equation of motion) of SDOF systems a) By equivalent energy method

  3. Example: Find equivalent stiffness using “Equivalent energy method”

  4. Example: Find equivalent mass using “Equivalent energy method”

  5. Example: Find equation of motion of the following system by using Equivalent energy method.

  6. b) By Newton’s Second Law Equation of motion (Governing equation)

  7. Free-Body Diagram (FBD) FBD System

  8. Example: Find equation of motion of the following system by using Newton’s Second Law.

  9. Example: Find equation of motion of the following system by using Newton’s Second Law. c c

  10. Example: Find equation of motion of the following system by using Newton’s Second Law.

  11. Example: Find governing equations by a) Equivalent energy b) Newton’s Second Law by defining equivalent mass, stiffness and damping constant SOLVED DURING THE CLASS

  12. Do it yourself ! Do it yourself ! Example:Show that the system’s equation of motion is • By equivalent energy method • By Newton method

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