1.3. Free Vibration of SDOF Systems

Try these first

1. 1.

   Define Free Vibration in your own words.

   Hint

   Think about what happens after you push a swing.

2. 2.

   What does SDOF stand for?

   Hint

   Consider how many coordinates describe its motion.

3. 3.

   What is the equation of motion for an SDOF system during free vibration?

   • mx¨ + kx = 0
   • mx¨ + cx˙ + kx = 0
   • mx¨ = F

   Hint

   Consider what happens in the absence of external forces.

4. 4.

   True or False: Natural frequency is independent of the mass and stiffness of the system.

   • True
   • False

   Hint

   Think about the relationship between mass, stiffness, and oscillation.

5. 5.

   Design a simple SDOF system with a mass of 5 kg and a spring constant of 250 N/m. Calculate the natural frequency and discuss the implications of resonance in structure design.

   Hint

   Use the formula for natural frequency and relate it to design principles.

6. 6.

   A system is undergoing forced harmonic excitation with a frequency that is slightly different from its natural frequency. Describe the behavior observed and how damping can influence this behavior.

   Hint

   Relate the concepts of damping, resonance, and real-world system behavior.