Two identical pendulums oscillate with a constant phase difference `(pi)/(4)` and same amplitude. If the maximum velocity of one is v, the maximum velocity of the other will be.

Options

A. v
B. `sqrt2v`
C. 2v
D. `(v)/(sqrt2)`

Answer

To solve the problem, we need to analyze the motion of two identical pendulums that oscillate with a constant phase difference of \( \frac{\pi}{4} \) and the same amplitude. We are asked to find the maximum velocity of the second pendulum if the maximum velocity of the first pendulum is \( v \).

### Step-by-Step Solution:

1. **Understanding Maximum Velocity**:
The maximum velocity (\( V_{max} \)) of a pendulum can be expressed using the formula:
\[ V_{max} = \omega A \]
where \( \omega \) is the angular frequency and \( A \) is the amplitude.

2. **Identical Pendulums**:
Since both pendulums are identical, they have the same length \( l \). The angular frequency \( \omega \) for a simple pendulum is given by:
\[ \omega = \sqrt{\frac{g}{l}} \]
where \( g \) is the acceleration due to gravity.

3. **Same Amplitude**:
The problem states that both pendulums have the same amplitude \( A \). Therefore, both pendulums will have the same angular frequency \( \omega \) and the same amplitude \( A \).

4. **Maximum Velocity Calculation**:
Since both pendulums have the same \( \omega \) and \( A \), we can conclude that their maximum velocities will also be the same. Thus, if the maximum velocity of the first pendulum is \( v \), then the maximum velocity of the second pendulum will also be:
\[ V_{max,2} = \omega A = v \]

5. **Conclusion**:
Therefore, the maximum velocity of the second pendulum is also \( v \).

### Final Answer:
The maximum velocity of the other pendulum will be \( v \).