9.5. Unit Impulse Response Function (Green’s Function)

Try these first

1. 1.

   What is the impulse response function also known as?

   Hint

   Think about the function that describes systems' responses.

2. 2.

   What does a unit impulse input represent?

   Hint

   Remember the mathematical representation of an impulse.

3. 3.

   What does the impulse response function help to analyze?

   • Only damped systems
   • Responses to arbitrary forces
   • Static forces

   Hint

   Consider the broader implications of the impulse response.

4. 4.

   True or False: Green's Function is only applicable to undamped systems.

   • True
   • False

   Hint

   Remember the definition of linear time-invariant systems.

5. 5.

   Given a system with a known impulse response function h(t) = e^{-t} cos(2t), compute the response x(t) to an external force F(t) = sin(t) for 0 ≤ t ≤ 10.

   Hint

   Don't forget to break down the convolution process step by step.

6. 6.

   If a structure responds to an impulse at t=0 with a maximum displacement of 0.5m and then gradually decreases, describe how you would assess its performance using impulse response functions.

   Hint

   Focus on data collection methods and modeling techniques.