Diracs delta equation - general interpretation


by finitefemmet
Tags: delta, dirac, function, interpretation
finitefemmet
finitefemmet is offline
#1
Apr30-12, 11:19 AM
P: 13
Im really just searching for a general explanation!

If you are solving a pretty standard left hand side differential equation, but a diracs delta function on the right hand side. I am abit confused about how to interpret this.

If this is the case for the right hand side:

r(t) = Diracs (t) ,for 0≤ t<T with the period T=2∏

Think of this as an periodic outside force on a spring system, now I dont know how to interpret this. Does this mean that r(t) repeats itself, at t=0, t=2∏ and so on. Or that the diracs delta equation only excists between 0 and 2∏?

Since its a diracs delta equation, it cannot work over a longer time interval? Since its an instant impuls over an extremely small time space.

If anyone could shed some light over this, I would be most gratefull.
I am not looking for a solution, just general information on how to interpret this information with the diracs delta function

Thank you, and excuse my poor english!
Phys.Org News Partner Science news on Phys.org
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
Office_Shredder
Office_Shredder is offline
#2
Apr30-12, 04:05 PM
Mentor
P: 4,499
They mean that the function repeats itself
HallsofIvy
HallsofIvy is offline
#3
Apr30-12, 09:36 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882
For every positive integer k, let fk(t)=
0 for 2(n-1)pi+ 1/k to 2npi- 1/k,
k/2 for 2npi- 1/k to 2npi+ 1/k

for n any positive integer. The periodic "delta function" is the limit of fk(x) as k goes to infinity. Essentially, that gives a "delta function" at every multiple of 2pi.

finitefemmet
finitefemmet is offline
#4
May1-12, 01:28 AM
P: 13

Diracs delta equation - general interpretation


Thank you both;)


Register to reply

Related Discussions
Geometric interpretation of an equation Calculus & Beyond Homework 2
Recast of an expression containing Diracs [tex]\delta[/tex]-function Calculus 2
Double integral of product of Diracs Calculus 2
inhomogeneous wave equation: physical interpretation Differential Equations 0
simple calculus - interpretation Euler-Lagrange equation Calculus & Beyond Homework 2