Solving an Electric Circuit with Kirchhoff's Voltage Law

[pokgai]

Homework Statement

An electric circuit consists of a resistor with a resistance of 12 ohms, a capacitor with
a capacitance of 0:1 farads and an inductor with an inductance of 2 henry connected in
series with a voltage source of 52 cos t volts. Initially the charge on the capacitor is 3
coulombs and the current in the circuit is zero.
(a) Using Kirchho's voltage law, show that the charge q(t) coulombs on the capacitor
at time t seconds satisfies
d2q/dt2 +6dq/dt+5q = 26 cos t

Homework Equations

V-iR-q/c-Ldi/dt=0

The Attempt at a Solution

It's pretty basic in that you just plug in the values.
52cos(t)-dq/dt12-q/0.1-2di/dt=0
The only thing I don't understand is the relation with di/dt. I am doing calculus and as such I am not familiar with physics. Just wondering how does that di/dt become d^2q/dt^2.

Cheers

 

[ehild]

The current i is the derivative of the charge q with respect to time:

i=dq/dt.

di/dt is the derivative of i with respect to time, that is

di/dt=d(di/dt)/dt,

it is called "the second derivative" of q and denoted as

d^2d/dt^2.

ehild