14.2.1. Mathematical Modeling

Try these first

1. 1.

   What does the mass represent in a mass-spring-damper system?

   Hint

   Think about what the structure's weight would influence.

2. 2.

   What effect does damping have on vibrations?

   Hint

   Consider how dampers in cars reduce shake during driving.

3. 3.

   What does the term 'natural frequency' refer to in an SDOF system?

   • The frequency of an external force
   • The inherent vibrational frequency of a system
   • The sum of stiffness and mass

   Hint

   Think about how a guitar string vibrates when plucked.

4. 4.

   True or False: More damping results in higher amplitudes of vibration.

   • True
   • False

   Hint

   Consider how shocks are absorbed in car suspensions.

5. 5.

   A 15 kg mass is attached to a spring with a stiffness of 300 N/m. Calculate the natural frequency of this system and explain its implications for structural design.

   Hint

   Use the relationship between mass and stiffness to derive frequency.

6. 6.

   Discuss how you would model a tall building as an SDOF system to evaluate its response to an earthquake. Consider mass, stiffness, damping, and natural frequency in your answer.

   Hint

   Build from base physical principles to arrive at a complete structural model.