The resonance frequency of a certain RLC series circuit is `omega_(0)` . A source of angular frequency ` 2 omega_(0)` is inserted into the circuit. After transients die out, the angular frequency of current oscillation is

Options

A. `(omega_(0))/(2)`
B. `omega_(0)`
C. `2omega_(0)`
D. `1.5omega_(0)`

Answer

To solve the problem, we need to analyze the behavior of the RLC series circuit when a source of angular frequency \( 2\omega_0 \) is applied after the transients have died out. We will follow these steps:

### Step-by-Step Solution:

1. **Identify the Resonance Frequency**:
The resonance frequency of the RLC circuit is given as \( \omega_0 \).

2. **Understand the Input Frequency**:
A source of angular frequency \( 2\omega_0 \) is introduced into the circuit.

3. **Analyze the Behavior After Transients**:
After the transients die out, the circuit will oscillate at a frequency that is influenced by both the resonance frequency and the input frequency.

4. **Calculate the Average Frequency**:
The angular frequency of the current oscillation can be determined by taking the average of the resonance frequency and the applied frequency:
\[ \text{Average Frequency} = \frac{\omega_0 + 2\omega_0}{2} \]

5. **Simplify the Expression**:
Simplifying the average frequency:
\[ \text{Average Frequency} = \frac{3\omega_0}{2} = 1.5\omega_0 \]

6. **Conclusion**:
Therefore, the angular frequency of the current oscillation after the transients die out is \( 1.5\omega_0 \).

### Final Answer:
The angular frequency of current oscillation after the transients die out is \( 1.5\omega_0 \).