Calculating Capacitance of LC Circuit

[omer10000]

1. Homework Statement

Calculate capacitance of LC Circuit where:

Inductor - 30H
Capacitance voltage fully charged goes to zero in 20 seconds

2. Homework Equations

Main Eq: V=V. *cost(ωt) where V is final Voltage, V. = Voltage initial, ω = resonant angular frequency

ω = 1/√(LC) = 2∏f

f. = 1/2∏√(LC) --> resonance frequency

3. The Attempt at a Solution

Calculated f=1/80 =0.0125Hz as voltage of capacitor takes 20s to deplete 1/4 cycle
∴ ω = 2∏*0.0125=0.0785

Rearranged angular frequency equation to solve for C
∴C=1/(ω^2 * L) = 5.404F

Since Voltage = 0 after t = 20s = 1/3min,

V=V. *cost(ωt)
0=V.*cos(0.0785*(1/3))

Since the whole equation is multiplication, calculating V. would not be required since if cos equaled 0 then so would the whole right hand side of the equation. However cos equals close to 1 and therefore I'm stuck.

Please help

Thank you

 

[omer10000]

Mistake has been found, since ω is in rad/s, t needs to be in s, ∴

V=V.*cos(ωt)
0=V.*cos(0.0785*20)
0=V.*0.00
0=0

..so it was really an error in calculating and not method.

Therefore C=5.404Farads.

Thank you