2.3. Free and Forced Vibrations with Damping

Try these first

1. 1.

   Define free vibration.

   Hint

   Think of a pendulum swinging.

2. 2.

   What is forced vibration?

   Hint

   Consider what happens in an earthquake.

3. 3.

   What describes free vibration?

   • Vibrations due to external forces
   • Vibrations without external forces
   • Vibrations with significant damping

   Hint

   Think about how a swing moves.

4. 4.

   True or False: Damping increases peak amplitudes during resonance.

   • True
   • False

   Hint

   Recall how damping affects oscillations.

5. 5.

   Explain how you would model a damped harmonic oscillator. Include the parameters and forces involved.

   Hint

   Focus on how each part of the equation relates to physical properties.

6. 6.

   Consider a building designed to withstand vibrations during an earthquake. Calculate the expected oscillation decay given specific damping ratio values.

   Hint

   Use the formulas from the session to establish relationships in your calculations.