Finding angular frequency in electric circuit

[sodper]

Homework Statement

At a certain angular frequency, the phase difference between [tex]U_{2}[/tex] and [tex]U_{1}[/tex] is [tex]180^{\circ}[/tex].
a) Calculate this angular frequency
b) Calculate [tex]U_{2}[/tex] at this angular frequency

See the attachment for circuit configuration.

Homework Equations

Ohms law: [tex]U = Z \cdot I[/tex]
Voltage: [tex]U = \hat{U} cos(\omega t + \alpha) [/tex]

The Attempt at a Solution

I can't seem to find the relation between phase difference and angular frequency.

I've tried to compute the equivalent double-pole, separating the coil with voltage [tex]U_2[/tex] from the rest och the circuit, with the following result:

Idle current:
[tex]U_t = \frac{\omega^2 L^2 + Rj\omega L}{R^2 + \omega^2 L^2} U_1[/tex]

Equivalent impedance:
[tex]Z_0 = \frac{\omega^2 RCL - R - j\omega L}{\omega^2 LC - j\omega RC}[/tex]

And from this I've calculated [tex]U_{2}[/tex]:
[tex]U_{2} = \frac{j\omega L}{Z_0 + j\omega L} U_t[/tex]

But as stated, I can't find the relation between angular frequency and phase difference. How do I use the phase difference?

 

[sodper]

I'm stuck here. Does anyone have a suggestion?

 

[Moetasim]

The relation between angular frequency and phase difference in an electric circuit can be found using the formula: \phi = \tan^{-1}\left(\frac{\omega L}{R}\right), where \phi is the phase difference, \omega is the angular frequency, L is the inductance, and R is the resistance in the circuit. In this case, since the phase difference is 180^{\circ}, we can set \phi = \pi and solve for \omega. Once we have the value of \omega, we can use the formula for voltage, U = \hat{U} cos(\omega t + \alpha), to calculate the voltage U_{2} at this angular frequency.