Diracs delta equation  general interpretationby finitefemmet Tags: delta, dirac, function, interpretation 

#1
Apr3012, 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! 



#2
Apr3012, 04:05 PM

Mentor
P: 4,499

They mean that the function repeats itself




#3
Apr3012, 09:36 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882

For every positive integer k, let fk(t)=
0 for 2(n1)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. 



#4
May112, 01:28 AM

P: 13

Diracs delta equation  general interpretation
Thank you both;)



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