9.1. Impulse Force and its Mathematical Representation

Try these first

1. 1.

   Define impulse in the context of forces.

   Hint

   Consider situations where forces are rapidly applied.

2. 2.

   What is the Dirac delta function?

   Hint

   Think about how it relates to instant forces.

3. 3.

   What does the impulse signify in dynamic systems?

   • A continuous force
   • A force of very large magnitude acting over a short period
   • A force that does not change

   Hint

   Think about it in terms of earthquake forces.

4. 4.

   True or False: The Dirac delta function is zero for all points except at zero.

   • True
   • False

   Hint

   Consider what happens to the function at various points.

5. 5.

   Considering a structure that undergoes an impulse response due to an earthquake, calculate the impulse provided that the peak force experienced was 2000 N over 0.1 seconds.

   Hint

   Think about how impulse relates force and time.

6. 6.

   Discuss how the response of a building to seismic waves can be modeled using the sifting property of the Dirac delta function and provide an example calculation.

   Hint

   Consider how impulses represent greater forces at specific time points in your model.