The maximum velocity of a simple harmonic motion represented by `y = 3 sin (100t + (pi)/(6))` is given by

Options

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

Answer

To find the maximum velocity of the simple harmonic motion represented by the equation \( y = 3 \sin(100t + \frac{\pi}{6}) \), we can follow these steps:

### Step 1: Identify the parameters from the SHM equation
The general form of the simple harmonic motion (SHM) equation is:
\[ y = A \sin(\omega t + \phi) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( \phi \) is the phase constant.

From the given equation \( y = 3 \sin(100t + \frac{\pi}{6}) \), we can identify:
- Amplitude \( A = 3 \)
- Angular frequency \( \omega = 100 \)

### Step 2: Use the formula for maximum velocity
The maximum velocity \( V_{\text{max}} \) in simple harmonic motion is given by the formula:
\[ V_{\text{max}} = A \cdot \omega \]

### Step 3: Substitute the values into the formula
Now, substituting the values of \( A \) and \( \omega \) into the formula:
\[ V_{\text{max}} = 3 \cdot 100 \]

### Step 4: Calculate the maximum velocity
Calculating the above expression:
\[ V_{\text{max}} = 300 \]

### Conclusion
Thus, the maximum velocity of the simple harmonic motion is:
\[ \boxed{300} \]