12.4.3. Shifting Property

Try these first

1. 1.

   What is the shifting property of the Dirac delta function?

   Hint

   Think about where this delta function has its maximum value.

2. 2.

   How does the shifting property relate to evaluating functions?

   Hint

   Consider how this could simplify integration.

3. 3.

   What does the shifting property of the delta function indicate?

   • It spreads over an interval
   • It is concentrated at a point
   • It is always zero

   Hint

   Think about where the function has its maximum value.

4. 4.

   True or False: The shifting property is unrelated to the sifting property.

   • True
   • False

   Hint

   Look for connections between how each property functions.

5. 5.

   If a load of P=10N is applied at x=5m on a beam, express the load function in terms of the Dirac delta function and integrate to find its effect over a 10m beam.

   Hint

   Consider how localized loads work in influence diagrams.

6. 6.

   Discuss how the ‘shifting property’ can impact the solution of a dynamic system under impulse loading modeled by a delta function. Illustrate with equations.

   Hint

   How do you express forces acting instantaneously in dynamics?