The switch in the figure below is connected to point a for a long time. (the pic

Question

The switch in the figure below is connected to point a for a long time.

(the picture is complete just the line that's connecting the whole circuit is not showing up for some reason..)

As shown, R = 13.0 , L = 0.101 H, E = 18.00 V and C = 1.42 F.
At t = 0, the switch is thrown to point b:

a) What is the frequency of oscillation of the LC circuit?

b) What is the maximum charge that appears on the capacitor?

c) What is the maximum current in the inductor?

d) What is the total energy the circuit possesses at t = 3.35 s?

Explanation / Answer

f=1/2LC

f=420.25 Hz

as Q=Qocoswt

at wt=0

Q=Qo

Q=CV

Q=25.56x10-6 C

i=-wQsinwt

at wt=90

imax=-wQmax

imax=-2fQmax

imax=67.49 mA

E=Q2/2C

and

Q at 3.35 sec is

Q=Qocos(3.15x2xfx)

Q=25.56x10-6 C

so E=9J

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