The amplitude (A) of damped oscillator becomes half in 5 minutes. The amplitude after next 10 minutes will be

Options

A. A
B. A/8
C. A/4
D. 4A

Answer

To solve the problem, we need to understand the behavior of a damped oscillator and how its amplitude decreases over time.

### Step-by-Step Solution:

1. **Understanding the Problem**:
The amplitude \( A \) of a damped oscillator becomes half in 5 minutes. We need to find the amplitude after the next 10 minutes.

2. **First Interval (0 to 5 minutes)**:
- Initial Amplitude: \( A \)
- After 5 minutes, the amplitude becomes half:
\[ A_1 = \frac{A}{2} \]

3. **Second Interval (5 to 10 minutes)**:
- Now, we consider the next 5 minutes (from 5 to 10 minutes).
- The amplitude will again become half of its current value:
\[ A_2 = \frac{A_1}{2} = \frac{\frac{A}{2}}{2} = \frac{A}{4} \]

4. **Third Interval (10 to 15 minutes)**:
- Now, we consider the next 5 minutes (from 10 to 15 minutes).
- The amplitude will again become half of its current value:
\[ A_3 = \frac{A_2}{2} = \frac{\frac{A}{4}}{2} = \frac{A}{8} \]

5. **Final Result**:
- After 15 minutes (5 minutes + 5 minutes + 5 minutes), the amplitude of the damped oscillator will be:
\[ A_3 = \frac{A}{8} \]

### Conclusion:
The amplitude after the next 10 minutes (which is 15 minutes from the start) will be \( \frac{A}{8} \).