The displacement equation of a particle performing S.H.M. is x = 10 sin `(2pit+(pi)/(6))`m. Then the initial displacement of a particle is

Options

A. 5 m
B. 2.5 m
C. 0.5 m
D. 0.25 m

Explanation

To find the initial displacement of a particle performing simple harmonic motion (S.H.M.) given the displacement equation \( x = 10 \sin(2\pi t + \frac{\pi}{6}) \) m, we will evaluate the equation at \( t = 0 \).

### Step-by-Step Solution:

1. **Identify the Displacement Equation**:
The displacement of the particle is given by:
\[ x = 10 \sin(2\pi t + \frac{\pi}{6}) \]

2. **Substitute \( t = 0 \)**:
To find the initial displacement, substitute \( t = 0 \) into the equation:
\[ x(0) = 10 \sin(2\pi \cdot 0 + \frac{\pi}{6}) \]

3. **Simplify the Equation**:
This simplifies to:
\[ x(0) = 10 \sin(\frac{\pi}{6}) \]

4. **Calculate \( \sin(\frac{\pi}{6}) \)**:
We know that:
\[ \sin(\frac{\pi}{6}) = \frac{1}{2} \]

5. **Substitute the Value of \( \sin(\frac{\pi}{6}) \)**:
Now, substitute this value back into the equation:
\[ x(0) = 10 \cdot \frac{1}{2} = 5 \text{ m} \]

6. **Conclusion**:
Therefore, the initial displacement of the particle is:
\[ x(0) = 5 \text{ m} \]

### Final Answer:
The initial displacement of the particle is **5 m**.