Actually yes,
dI/dt = d^2Q/dt^2
so the equation is
2(d^2Q/dt^2) + 12(dQ/dt) + 10Q = 12 sin(t)
which is a second order linear differential equation.
Hi all,
I am unsure of what to do with this one.
I have been given some conditions in an electric circuit. Due to Kirchoff's law I have calculated the differential equation to be:
2(dI/dt) + 12(dQ/dt) + 10Q = 12 sin(t)
where 12 sin(t) is the supplied voltage.
Im supposed to find Q at time t with initial conditions Q(0) = 0.2 and I(0)=0.
Is this a first order linear differential equation? Or is it classified as something else?
What confuses me is that it has 2(dI/dt) + 12(dQ/dt). I was thinking that perhaps dI/dt = d^2Q/dt^2 or vise versa but really im not sure.
[quote=woody198403;148103]Actually yes,
dI/dt = d^2Q/dt^2
so the equation is
2(d^2Q/dt^2) + 12(dQ/dt) + 10Q = 12 sin(t)
This is a 2nd order linear DE
So first we need to solve the associated homogenious equation
so the two roots are m=-1 and m=-5
This gives the complimentry solution
Now we need to find the particular solution
since the driving function is 12sin(t)
we know the particular solution is of the form
taking a few derivatives and plugging into the non homogenious equation and solvinf for A and B will finish the problem.
Good luck.