9.3. Free Vibration Response of Undamped SDOF System to Unit Impulse

Try these first

1. 1.

   Define impulse in the context of dynamics.

   Hint

   Think about forces that occur suddenly.

2. 2.

   What does the unit impulse function represent mathematically?

   Hint

   Consider how it models instantaneous forces.

3. 3.

   What is the mathematical representation of a unit impulse?

   • λ(t)
   • α(t)
   • δ(t)

   Hint

   Think about the functions we've discussed.

4. 4.

   True or False: An undamped SDOF system will oscillate indefinitely.

   • True
   • False

   Hint

   Consider what happens when there's no energy loss.

5. 5.

   A mass-spring system has a mass of 2 kg and a spring constant of 8 N/m. Calculate the displacement response x(t) when a unit impulse is applied.

   Hint

   Use the relationship between mass, spring constant, and the natural frequency.

6. 6.

   Explain the consequence of an undamped response in structural dynamics. What design principles should be applied?

   Hint

   Think about how adding dampers might change the response.