The displacement of a particle executing SHM is given by
y=0.5 sin100t cm . The maximum speed of the particle is

Options

A. `200 cm s^(-1)`
B. `100 cm s^(-1)`
C. `50 cm s^(-1)`
D. `5.25 cm s^(-1)`

Answer

To find the maximum speed of a particle executing simple harmonic motion (SHM) given by the displacement equation \( y = 0.5 \sin(100t) \) cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the parameters from the displacement equation**:
The given displacement equation is:
\[ y = 0.5 \sin(100t) \]
Here, the amplitude \( a \) is \( 0.5 \) cm, and the angular frequency \( \omega \) is \( 100 \) rad/s.

2. **Recall the formula for maximum speed in SHM**:
The maximum speed \( v_{\text{max}} \) of a particle in SHM is given by the formula:
\[ v_{\text{max}} = a \omega \]
where \( a \) is the amplitude and \( \omega \) is the angular frequency.

3. **Substitute the values into the formula**:
Now we can substitute the values of \( a \) and \( \omega \) into the formula:
\[ v_{\text{max}} = 0.5 \, \text{cm} \times 100 \, \text{rad/s} \]

4. **Calculate the maximum speed**:
Performing the multiplication:
\[ v_{\text{max}} = 50 \, \text{cm/s} \]

5. **Conclusion**:
The maximum speed of the particle is \( 50 \, \text{cm/s} \).

### Final Answer:
The maximum speed of the particle is \( 50 \, \text{cm/s} \).