- #1
longball
- 5
- 0
setting a sinusoidal voltage term, the ODE can be written as
(d^2 i)/(d t^2 ) + 25i = A0 sin (ϖt)
assuming that ϖ^2 ≠ 25, determine the current i in terms of the parameters (ϖ and A0) and the variable t when the initial conditions are
i(0) = di/dt (0) = 0
i really don't have much of an idea what to do here.
so far i have found
L.F ic= Acos(5t)+Bsin(5t)
P.S ip = acos(ϖt) + bsin (ϖt)
ip' = -ϖasin (ϖt) + ϖbcos (ϖt)
ip'' = -2ϖacos (ϖt) - 2ϖbsin (ϖt)
therefore
[-2ϖacos (ϖt) - 2ϖbsin (ϖt)] + [acos(ϖt) + bsin (ϖt)] = A0 sin (ϖt)
any help or further guidance to the work i have done would be much appreciated
(d^2 i)/(d t^2 ) + 25i = A0 sin (ϖt)
assuming that ϖ^2 ≠ 25, determine the current i in terms of the parameters (ϖ and A0) and the variable t when the initial conditions are
i(0) = di/dt (0) = 0
i really don't have much of an idea what to do here.
so far i have found
L.F ic= Acos(5t)+Bsin(5t)
P.S ip = acos(ϖt) + bsin (ϖt)
ip' = -ϖasin (ϖt) + ϖbcos (ϖt)
ip'' = -2ϖacos (ϖt) - 2ϖbsin (ϖt)
therefore
[-2ϖacos (ϖt) - 2ϖbsin (ϖt)] + [acos(ϖt) + bsin (ϖt)] = A0 sin (ϖt)
any help or further guidance to the work i have done would be much appreciated