The maximum velocity of a simple harmonic motion represented by `y="sin"(100t+(pi)/(6))` is given by

Options

A. 300 units
B. `(3pi)/(6)` units
C. 100 units
D. `(pi)/(6)` units

Explanation

To find the maximum velocity of the simple harmonic motion represented by the equation \( y = \sin(100t + \frac{\pi}{6}) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Parameters**:
The given equation is in the form of \( y = a \sin(\omega t + \phi) \). Here, we can identify:
- Amplitude \( a = 1 \) (since the coefficient of sine is 1)
- Angular frequency \( \omega = 100 \) (the coefficient of \( t \))
- Phase constant \( \phi = \frac{\pi}{6} \)

2. **Write the Formula for Maximum Velocity**:
The maximum velocity \( v_{\text{max}} \) of a particle in simple harmonic motion can be calculated using the formula:
\[ v_{\text{max}} = a \omega \]

3. **Substitute the Values**:
Now, substituting the values of amplitude \( a \) and angular frequency \( \omega \):
\[ v_{\text{max}} = 1 \times 100 = 100 \text{ units} \]

4. **Conclusion**:
Therefore, the maximum velocity of the simple harmonic motion represented by the equation \( y = \sin(100t + \frac{\pi}{6}) \) is \( 100 \text{ units} \).

### Final Answer:
The maximum velocity is \( 100 \text{ units} \).

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