12.1. Concept and Informal Definition

Try these first

1. 1.

   What is the value of δ(x) for x not equal to 0?

   Hint

   Remember the definition of the Dirac delta function.

2. 2.

   What does the integral of δ(x) over the entire real line equal?

   Hint

   Consider the area under the curve.

3. 3.

   What value does δ(x) take when x is not equal to 0?

   • 1
   • 0
   • ∞

   Hint

   Think about the function's definition.

4. 4.

   True or False: The Dirac delta function integrates to one over the real line.

   • True
   • False

   Hint

   Consider the area under the curve.

5. 5.

   Consider a bridge where a car passes over it at time t = 0, producing a load represented by δ(t). How would you use the Dirac delta function to analyze the effect on the bridge's structure?

   Hint

   Think about how the impulse behaves over time.

6. 6.

   A concentrated load P is applied at point x = a along a beam described by the differential equation. How would you set up the governing equation including the Dirac delta function?

   Hint

   Focus on how to represent point loading mathematically.