15.7. Important Notes

Try these first

1. 1.

   Explain the purpose of the Final Value Theorem.

   Hint

   Think about the behavior of systems over a long duration.

2. 2.

   What does the Initial Value Theorem help to determine?

   Hint

   Consider the starting point of a function.

3. 3.

   What does the Final Value Theorem calculate?

   • Initial value of f(t)
   • Final value of f(t)
   • Derivative of f(t)

   Hint

   Consider the behavior of f(t) as time progresses.

4. 4.

   True or False: FVT can be used if poles of sF(s) lie in the right half of the complex plane.

   • True
   • False

   Hint

   Think about the stability conditions discussed.

5. 5.

   Given f(t) = e^(-3t) * cos(4t), determine if you can apply FVT and calculate the steady-state value if possible.

   Hint

   Focus on the damping factor vs frequency.

6. 6.

   Evaluate if f(t) = e^(2t) fits the criteria for FVT application and identify its limitations.

   Hint

   Examine the exponential growth behavior.