Earthquake Engineering - Vol 1 | 7. Free Vibration of Single Degree of Freedom (SDOF) System by Abraham | Learn Smarter
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

7. Free Vibration of Single Degree of Freedom (SDOF) System

7. Free Vibration of Single Degree of Freedom (SDOF) System

The chapter provides a comprehensive overview of the Free Vibration of Single Degree of Freedom (SDOF) systems, emphasizing foundational concepts such as the definition and equations of motion, solutions to these equations, natural frequency, and the impacts of mass and stiffness on vibration behavior. It also explores real-world applications in earthquake engineering and the significance of understanding both undamped and damped systems in structural design.

20 sections

Enroll to start learning

You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

Navigate through the learning materials and practice exercises.

  1. 7
    Free Vibration Of Single Degree Of Freedom (Sdof) System

    This section introduces the concept of free vibration in a Single Degree of...

  2. 7.1
    Definition Of Free Vibration

    Free vibration refers to the natural oscillation of a mechanical system...

  3. 7.2
    Idealization Of Sdof System

    The idealization of a Single Degree of Freedom (SDOF) system focuses on its...

  4. 7.3
    Equation Of Motion For Free Vibration

    This section introduces the equation of motion for an undamped single degree...

  5. 7.4
    Solution To The Equation Of Motion

    This section presents the solution to the equation of motion for a Single...

  6. 7.5
    Natural Frequency And Time Period

    This section discusses the natural frequency and time period of a Single...

  7. 7.6
    Initial Conditions And System Response

    This section discusses how initial displacement and velocity define the...

  8. 7.7
    Graphical Representation Of Motion

    The section discusses the sinusoidal and periodic motion of an undamped SDOF...

  9. 7.8
    Energy In Free Vibration

    In undamped free vibration, mechanical energy is conserved, with kinetic and...

  10. 7.9
    Effect Of Mass And Stiffness

    The effect of mass and stiffness on the natural frequency of a Single Degree...

  11. 7.10
    Resonance In Sdof Systems

    This section explains resonance in Single Degree of Freedom (SDOF) systems,...

  12. 7.11
    Real-World Application In Earthquake Engineering

    This section discusses how Single Degree of Freedom (SDOF) systems are...

  13. 7.12
    Damped Vs Undamped Free Vibration (Introduction To Damping)

    This section introduces the concept of damping in vibrational systems,...

  14. 7.13
    Logarithmic Decrement (Δ)

    Logarithmic decrement is a method for measuring damping in oscillating...

  15. 7.14
    Phase Plane Representation

    Phase plane representation is a method to visualize the motion of dynamical...

  16. 7.15
    Numerical Solution Of Free Vibration (Finite Difference Method)

    The finite difference method allows for the numerical solution of free...

  17. 7.16
    Modal Parameters And Experimental Determination

    The section discusses methods to experimentally determine a structure's...

  18. 7.17
    Vibration Isolation And Structural Implications

    This section focuses on vibration isolation techniques to protect structures...

  19. 7.18
    Role In Seismic Design Codes

    Seismic design codes utilize fundamental natural periods derived from SDOF...

  20. 7.19
    Case Studies And Real-World Observations

    This section discusses how case studies from past earthquakes inform our...

What we have learnt

  • Free vibration occurs without external forces after initial disturbance, governed by the mass-spring system dynamics.
  • Natural frequency and time period are fundamental properties influencing system oscillation in free vibration.
  • Real-world structures often experience damping, which alters vibration behavior critical to earthquake-resistant design.

Key Concepts

-- Free Vibration
The motion of a mechanical system allowed to vibrate naturally after an initial disturbance, without external forces.
-- Natural Frequency
The frequency at which a system naturally oscillates, determined by the mass and stiffness in an SDOF system.
-- Damping
The effect of energy dissipation in a system that leads to a decrease in the amplitude of oscillation.
-- Resonance
A phenomenon where a system vibrates with maximum amplitude at its natural frequency, often resulting in structural failure.
-- Logarithmic Decrement
A measure of damping in systems that quantifies the rate of amplitude decay over time.

Additional Learning Materials

Supplementary resources to enhance your learning experience.