a series R-L-C circuit connected to a generator that causes f = 1400 Hz oscillat

Question

a series R-L-C circuit connected to a generator that causes f = 1400 Hz oscillations in it. The generator is now removed and replaced with a switch which is set in the OFF position. The values of the other components remain the same, R = 4.47 ohm, L = 26.5 micro-Henry, and C = 680 micro-Farad. At time t = 0, the capacitor has been fully charged, Qmax = 150 millicoulomb, and then the switch is suddenly closed (ON position). Determine how long until the charge on the capacitor will be reduced to 25% of the initial value? Give your answer in the form "a.bc x 10^(x) " s

Explanation / Answer

the chage will oscillate in a sinusoidal way with frequency=1/(2*pi*sqrt(LC)=1185.61 Hz

then we can denote it by

Q=150*cos(1185.61*2*pi*t)

so to get Q=Q/4

150/4=150*cos(1185.61*2*pi*t)

t=10.13 ms

=1.0138*10^(-2)

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