T-Pain Is On A Boat: Re: [Electric Boats] Re: Innovation and Resonance

Understood by whom? These aren't your calcs, and I'll guess you haven't tested them, so because he's someone smarter, better educated, has a Wiki entry you trust them?

Apply them to a real world situation or two in different fields and then I'll agree, but hey your happy so what the hell.

On 23 May 2013 21:35, NIcholas Luker <nickluker@gmail.com> wrote:

On 24/05/2013, at 6:20 AM, "cire" <cirejay@hotmail.com> wrote:

-
> From: Julian Webb
> To: electricboats@yahoogroups.com
> Sent: Thursday, May 23, 2013 3:11 AM
> Subject: Re: [Electric Boats] "Batteries Not Included"
> SNIP...

> - To cut a long story short unless the importance of electrical and mechanical resonance in systems is appreciated, (which has no place, constant or symbol in any traditional calculations or formulas that I have ever seen) they cannot be understood or replicated.
>

Looks like its understood to me

yp=Atcos(5t)+Btsin(5t)+Ccos(t)+Dsin(t).

Working out the first and second differentials:

y′py′′p==Acos(5t)+Bsin(5t)−5Atsin(5t)+5Btcos(5t)−Csin(t)+Dcos(t),−10Asin(5t)+10Bcos(5t)−25Atcos(5t)−25Btsin(5t)−Ccos(t)−Dsin(t).

On substituting into the equation we expect all the tcos(5t) and tsin(5t) terms to cancel:

−10Asin(5t)+10Bcos(5t)+24Ccos(t)+24Dsin(t)=2sin(5t)+cos(t).

We can see that both B=0 and D=0, therefore we don't need these terms in the particular solution. If we had been clever and thought ahead we may have been able to foresee this and save ourselves some work. This sort of insight should hopefully come with practice; if in doubt include all the terms. From above we can also see A=−15and C=124 giving us:

yp=124cos(t)−t5cos(5t),

and full solution:

y=yc+yp=Acos(5t)+Bsin(5t)+124cos(t)−t5cos(5t).