One more nudge, please...

[hank]

(5.1.48)
Find the charge on the capacitor and the current in the given LRC series circuit. Find the max charge on the capacitor.
L = 1h, R = 100 ohms, C = 0.004f, E(T) = 30V, q(0) = 0, i(0) = 2A.

Here we go...

Lq" + Rq' + q/C = E(t)
q" + 100q' + 2500q = 30
m^2 +100m + 2500 = 0 //auxiliary equation
(m + 50)^ 2 = 0 => m1 = m2 = -50
qc = Ae^-50t + Bte^-50t //Complimentary equation, A and B are constants.

//Using annihilator operator D,
Dq = D30 = 0
So, qp =C //particular solution
//Using method of undetermined coefficents to find value for C:
2500C = 30 => C = 3/250

So,
q(t) = Ae^-50t + Bte^-50t + (3/250)

//Time to find values for A and B:
q(0) = 0 = A + (3/250) => A = -3/250
i(0) = q'(0) = 2 = -50A + B => 2 = (-50)(-3/250) + B => B = (7/5) = (350/250) //Assuming i(t) = q'(t)

So, q(t) = (-3/250)e^-50t + (350/250)te^-50t + (3/250)

This is where I get bogged down.
I assume that I'm supposed to set the above to 0 and solve for t:

0 = -3e^-50t + 350te^-50t + 3 //Multiplying both sides by 250 to eliminate fractions
-3 = (e^-50t)(-3 + 350t)

And now I don't know where to go from here.

Thanks in advance!

 

[Deleted member 4993]

(5.1.48)
Find the charge on the capacitor and the current in the given LRC series circuit. Find the max charge on the capacitor.
L = 1h, R = 100 ohms, C = 0.004f, E(T) = 30V, q(0) = 0, i(0) = 2A.

Here we go...

Lq" + Rq' + q/C = E(t)
q" + 100q' + 2500q = 30
m^2 +100m + 2500 = 0 //auxiliary equation
(m + 50)^ 2 = 0 => m1 = m2 = -50
qc = Ae^-50t + Bte^-50t //Complimentary equation, A and B are constants.

//Using annihilator operator D,
Dq = D30 = 0
So, qp =C //particular solution
//Using method of undetermined coefficents to find value for C:
2500C = 30 => C = 3/250

So,
q(t) = Ae^-50t + Bte^-50t + (3/250)

//Time to find values for A and B:
q(0) = 0 = A + (3/250) => A = -3/250
i(0) = q'(0) = 2 = -50A + B => 2 = (-50)(-3/250) + B => B = (7/5) = (350/250) //Assuming i(t) = q'(t)

So, q(t) = (-3/250)e^-50t + (350/250)te^-50t + (3/250)

This is where I get bogged down.
I assume that I'm supposed to set the above to 0 and solve for t:

Why - what does your problem ask you to solve?

0 = -3e^-50t + 350te^-50t + 3 //Multiplying both sides by 250 to eliminate fractions
-3 = (e^-50t)(-3 + 350t)

And now I don't know where to go from here.

Thanks in advance!

 

[hank]

It wants me to find the charge of the capacitor and the max charge of the capacitor.

 

[Deleted member 4993]

It wants me to find the charge of the capacitor and the max charge of the capacitor.

So why would you say:

I assume that I'm supposed to set the above to 0 and solve for t:

 

[hank]

It wants me to find the charge of the capacitor and the max charge of the capacitor.

So why would you say:

I assume that I'm supposed to set the above to 0 and solve for t:

In an example similar to the problem that's what they did.

I assumed it was the same case.
Our book isn't very clear.

How should I be solving this problem?

 

[Deleted member 4993]

It wants me to find the charge of the capacitor and the max charge of the capacitor.

So why would you say:

I assume that I'm supposed to set the above to 0 and solve for t:

In an example similar to the problem that's what they did.

I assumed it was the same case.
Our book isn't very clear.

How should I be solving this problem?

Are you saying you forgot - how to find "maxima/minima" of a function?

See if the following statement makes sense and reminds you to do certain things:

For a function of single variable, you set the slope of the tangent to the function to zero - for maxima/minima. Then you test again to confirm whether it was a maxima or minima.