- #1
gramentz
- 16
- 0
Mass on vertical spring with force applied.
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= v2/2
dv/dt = 5sin(2t) - 8v2
dv/dt +8v2 = 5sin(2t)
8v2dv = 5sin (2t)dt
Integrated both sides:
(8/3)v3 = (-5/2)cos(2t)
v3 = (-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!
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= v2/2
dv/dt = 5sin(2t) - 8v2
dv/dt +8v2 = 5sin(2t)
8v2dv = 5sin (2t)dt
Integrated both sides:
(8/3)v3 = (-5/2)cos(2t)
v3 = (-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!