Analyzing an LC circuit

For a mass on a spring we applied Newton's Second Law to get:

ma = -kx

We can write this equation as:
m
d2x
dt2
= -kx

The solution to this equation is:

x(t) = A cos(wt)
The angular frequency is given by w2 =
k
m

For an LC circuit we follow a similar process. The equation we get from Kirchoff's loop rule is:
L
dI
dt
= –
Q
C

Write this as:
L
d2Q
dt2
= –
Q
C

The solution is:

Q(t) = Qo cos(wt)
where w2 =
1
LC

The inductance L of the circuit is analogous to what for the object oscillating on the spring?

  1. The mass of the object
  2. The spring constant
  3. The inverse of the spring constant
  4. The velocity of the object












The inductance is a measure of the inertia in the circuit, much like the mass of the object is a measure of its inertia. The inductor opposes any change in current; the object's mass opposes any change in velocity.

The capacitance C of the circuit is analogous to what for the object oscillating on the spring?

  1. The mass of the object
  2. The spring constant
  3. The inverse of the spring constant
  4. The velocity of the object












The capacitance acts like the inverse of the spring constant. The spring force has a magnitude
F = kx.

The potential difference plays the role of the force in the circuit, and:
DV = Q/C.