LC Circuit Oscillations: Check My Work and Find Energy and Frequency Details

[davegillmour]

I'm not too confident in my work for this problem, so I was wondering if someone could check it over for me.

Consider a circuit with 4 elements, C1=100micro farads, C2=50micro farads, L1=20mH, and L2=10mH. At t=0, the capacitors are charged with Q=0.01 Coulomb. There is initially no current. (all 4 are connected in series)

a) What are the voltages across the capacitors?
V1=(1/C1)Q=(1/100micro farads)0.01= 100 Volts
V2=(1/50micro farads)0.01= 200 Volts
b)How much electrical and magnetic energy, respectively is stored in the circuit initially?
Ue=electric energy=q^2/(2C)
1/C=1/C1 +1/C2 C=33.3micro Farads
0.01^2/(2*33.3micro farads)=1.50 J
Ub=magnetic energy=(L*i^2)/2
i(initial)=0 so magnetic energy=0
c)What is the total inductance of the circuit.
L=L1+L2=20mH+10mH= 30mH
d)What is the total capacitance?
1/C=1/C1 + 1/C2 C=33.3micro farads
e)What is the frequency of oscillations in the circuit?
w=sqrt[1/(LC)] = sqrt[1/(30mH * 33.3micro farads)] = 1000 rad/s
f)What is q(t)? Make sure it satisfies q(0)=Q
q(t) = Qcos(wt + phi)
q(t) = (0.01)Cos(1000t) <---is the phase constant zero?
g)Compute i(t)= dq/dt
dq/dt= -10Sin(1000t)
h)Compute di/dt=d^2(q)/dt^2
di/dt= -10000Cos(1000t)

Thanks a lot to anyone who can do me this favor.

 

[lightgrav]

yes, the phase constant is zero since qharge on Cap's is maximum at t=0.
This is verified by the current being zero at t=0 (from the sine).