Finding vC(t) for a Critical Damping RLC Circuit

[MattHorbacz]

Homework Statement

In the circuit in the following figure, the resistor is adjusted for critical damping. The initial capacitor voltage is 15 V, and the initial inductor current is 6 mA and R=1250 ohms

Find vC(t) for t≥0.
Express your answer in terms of t, where t is in milliseconds.

Homework Equations

i=c*dv/dt

The Attempt at a Solution

the only part of this problem i am not getting is solving for the constants with the given initial conditions... the 2 roots to the differential equation are -5000. so:
v(t)=C_1*e^(-5000t)+C_2*t*e^(-5000t)
and
dv/dt [at t=0+]=-5000*C_1+C_2=i/c=(6*10^-3)A/(320*10^-9 F)=18750 volts/s
v(0)=C_1=15V
so C_2 -5000*15=18750...C_2=93750
but apparently C_2 is actually equal to 56250...If the equation was C_2-5000*15=-18750, then i would get 56250...where am i going wrong?

 

[ehild]

As the charge flows away from the capacitor, I=-dQ/dt= - C dV/dt.

ehild