How to Find i(t) for an Inductor in an LC Circuit?

[Abdulwahab Hajar]

Homework Statement

In the figure given, find i(t) for the inductor
My problem is though when we found i(t) with a source we find the transient response and the steady state response...
I know how to do the transient response of an RLC circuit not an LC one... do i just consider R to be 0

Homework Equations

the damping factor is given as (1/RC) for a parallel RLC circuit
the frequency is given as 1/(√LC) which in this case is 1/2 am I right?

The Attempt at a Solution

There obviously is no damping factor therefore α = 0, however if R = 0 and we substitute for R in the damping factor equation we get infinity??
and for some reason the book says the frequency is 1/4... where did I go wrong??
Thank you

 

[NascentOxygen]

the damping factor is given as (1/RC) for a parallel RLC circuit

Is this the damping factor ζ or is it the Quality factor Q?

The frequency of ½ looks right, though you need to specify its units.

 

[Abdulwahab Hajar]

Is this the damping factor ζ or is it the Quality factor Q?

The frequency of ½ looks right, though you need to specify its units.

In my textbook it's the damping factor which is R/2L for series RLC circuits and 1/RC for parallel RLC circuits

 

[NascentOxygen]

In my textbook it's the damping factor which is R/2L for series RLC circuits and 1/RC for parallel RLC circuits

More commonly known as the attenuation factor, $\alpha$. Are you sure the last one isn't $\mathsf {\frac 1{2RC}}$?

wikipedia is a good resource for this, along with myriad others

 

[gneill]

Since the circuit in question does not contain any resistance it is unwise to apply the "standard" RLC circuit formulas. With R = 0, any derivations of quantities or terms that rely on a division by R will be undefined or infinite (in other words, nonsense).

A better approach might be to start from the beginning, writing the differential equation for the given circuit.

 

[Abdulwahab Hajar]

Since the circuit in question does not contain any resistance it is unwise to apply the "standard" RLC circuit formulas. With R = 0, any derivations of quantities or terms that rely on a division by R will be undefined or infinite (in other words, nonsense).

A better approach might be to start from the beginning, writing the differential equation for the given circuit.

Thank you

 

[Abdulwahab Hajar]

More commonly known as the attenuation factor, $\alpha$. Are you sure the last one isn't $\mathsf {\frac 1{2RC}}$?

wikipedia is a good resource for this, along with myriad others

Never mind, I found it
thanks ;)