A particle moves on y-axis according to the equation `y = 3A +B sin omegat`. Amplitude of motion is

Options

A. `3A`
B. `B`
C. `3A + B`
D. `sqrt(A^(2) + B^(2))`

Explanation

To find the amplitude of the motion described by the equation \( y = 3A + B \sin(\omega t) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Equation**:
The given equation is \( y = 3A + B \sin(\omega t) \).

2. **Recognize the Components**:
In this equation, \( 3A \) is a constant term, and \( B \sin(\omega t) \) represents the oscillatory part of the motion.

3. **Understand the Role of the Constant**:
The term \( 3A \) does not affect the amplitude of the oscillation; it simply shifts the entire motion vertically. The mean position of the oscillation is shifted to \( y = 3A \).

4. **Identify the Amplitude**:
The amplitude of simple harmonic motion is determined by the coefficient of the sine function. In this case, the coefficient of \( \sin(\omega t) \) is \( B \).

5. **Conclusion**:
Therefore, the amplitude of the motion is \( B \).

### Final Answer:
The amplitude of the motion is \( B \).

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