A particle executing simple harmonic motion along y -axis has its motion described by the equation `y = A sin (omega t )+ B`. The amplitude of the simple harmonic motion is

Options

A. A
B. B
C. A+B
D. `sqrt(A+B)`

Explanation

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

### Step-by-Step Solution:

1. **Identify the Components of the Equation**:
The equation given is \( y = A \sin(\omega t) + B \). Here, \( A \) represents the coefficient of the sine function, and \( B \) is a constant.

2. **Understand the Role of Each Component**:
- The term \( A \sin(\omega t) \) represents the oscillatory part of the motion, which is responsible for the simple harmonic motion (SHM).
- The term \( B \) is a constant that shifts the entire motion vertically. It does not affect the amplitude of the oscillation.

3. **Define Amplitude**:
The amplitude of simple harmonic motion is defined as the maximum displacement from the mean position. In this case, the mean position is shifted by \( B \).

4. **Determine the Amplitude**:
Since the amplitude is determined solely by the oscillatory part \( A \sin(\omega t) \), the amplitude of the motion is simply the coefficient \( A \). The constant \( B \) does not contribute to the amplitude.

5. **Conclusion**:
Therefore, the amplitude of the simple harmonic motion described by the equation \( y = A \sin(\omega t) + B \) is \( A \).

### Final Answer:
The amplitude of the simple harmonic motion is \( A \).