{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chapter6.page11

chapter6.page11 - Definition 4.1 The Dirac delta function...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
4. DELTA FUNCTION 11 The graph contains solutions for the following three cases, (1) No external force is applied(blue curve). (2) Force of sin(2 t ) is applied at first π seconds and turnoff(red curve). (3) Force of sin(2 t ) is constantly applied (green curve). The initial configuration is that the spring is at equilibrium position x (0) = 0 and is compressed at 1 unit speed (feet/s) x 0 (0) = - 1 . From the graph we can clearly see that when the force is turnoff at t = π its effect is immediately gone(as shown below)! 4. Delta Function Delta function is one of so-called generalized functions, which are not functions in ordinary sense but as an operators that sometimes can be represented by ordinary functions.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Definition 4.1 . The Dirac delta function at a, δ a ( t ) , is an op-erator that satisfies Z ∞ g ( t ) δ a ( t ) dt = g ( a ) for any continuous function g ( t ) . In Physics, if f ( t ) , a ≤ t ≤ b is a force that acts only during a short period of time interval [a, b], the impulse p of force f ( t ) is computed as Z b a f ( t ) dt. δ a ( t ) can be viewed as an instantaneous unit impulse that occurs pre-cisely at the instant t = a. And pδ a ( t ) is an instantaneous p units impulse that occurs precisely at the time t = a. δ a ( t ) is an important function used in modelling real phenomena, for example,...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online