27.7.3. Integration and Differentiation

Try these first

1. 1.

   What is integration in the context of seismograms?

   Hint

   Think about how we accumulate data over time.

2. 2.

   What does differentiation do?

   Hint

   Consider how we see changes over time.

3. 3.

   What does integration allow us to derive from acceleration data?

   • Velocity
   • Displacement
   • Both Velocity and Displacement

   Hint

   Recall how we use motion data.

4. 4.

   True or False: Differentiation can be used to find velocity from displacement data.

   • True
   • False

   Hint

   Think about how changes occur over time.

5. 5.

   Given a seismogram with acceleration data recorded during an earthquake, outline the mathematical steps to compute displacement at two significant intervals of time.

   Hint

   Focus on how you accumulate data over time using numerical integration.

6. 6.

   Describe how an engineer can use the differentiation of the displacement data to enhance a building's design against earthquake forces.

   Hint

   Consider the dynamic response of buildings when ground conditions change.