To calculate the maximum speed of a body performing simple harmonic motion, we can use the following formula:
\[ v_{\text{max}} = A \cdot \omega \]
where:
- \( v_{\text{max}} \) is the maximum speed,
- \( A \) is the amplitude of the motion,
- \( \omega \) is the angular frequency.
First, we need to determine the angular frequency \( \omega \). The angular frequency is related to the period \( T \) by the formula:
\[ \omega = \frac{2\pi}{T} \]
Given that the period \( T \) is 2 seconds, we can calculate \( \omega \):
\[ \omega = \frac{2\pi}{2} = \pi \]
Here, \( \pi \) is given as \( \frac{22}{7} \).
Next, we use the amplitude \( A \), which is 3.5 cm or 0.035 meters (since we need to work in SI units for speed in meters per second).
Now we can calculate the maximum speed:
\[ v_{\text{max}} = A \cdot \omega = 0.035 \cdot \pi = 0.035 \cdot \frac{22}{7} \]
Let's compute this:
\[ v_{\text{max}} = 0.035 \cdot \frac{22}{7} = 0.035 \cdot 3.142857 = 0.109999995 \approx 0.11 \, \text{m/s} \]
Therefore, the maximum speed of the body performing simple harmonic motion is approximately \( 0.11 \) meters per second.
