- #1

gramentz

- 16

- 0

dy/dt = v

dv/dt = 5sin(wt) - 16y

I am trying to figure out the velocity of this object at any given time when w= 2 rad/ sec. (Would ideally like to have it for any w and any t)

Did I do this correctly? (In calc 2, haven't had diff eq yet)

dv/dt = 5sin(2t)- 16y

y= v

^{2}/2

dv/dt = 5sin(2t) - 8v

^{2}

dv/dt +8v

^{2}= 5sin(2t)

8v

^{2}dv = 5sin (2t)dt

Integrated both sides:

(8/3)v

^{3}= (-5/2)cos(2t)

v

^{3}= (-15/16) cos(2t)

v= [tex]\sqrt[3]{ ((-15/16) cos (2t))}[/tex]

Did I do this correctly or even approach this the right way? Thanks for any help!