To calculate the maximum velocity of a small bob oscillating as a simple pendulum, we need to use the given data:
1. Amplitude [tex]\( A \)[/tex] = [tex]\( 5.0 \times 10^{-2} \)[/tex] meters
2. Period [tex]\( T \)[/tex] = 21 seconds
The formula for the maximum velocity ([tex]\( v_{\text{max}} \)[/tex]) of a simple pendulum is given by:
[tex]\[
v_{\text{max}} = \frac{2 \pi A}{T}
\][/tex]
where:
- [tex]\( A \)[/tex] is the amplitude,
- [tex]\( T \)[/tex] is the period,
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159.
Plugging in the given values:
[tex]\[
A = 5.0 \times 10^{-2} \, \text{m}
\][/tex]
[tex]\[
T = 21 \, \text{s}
\][/tex]
Now, substitute these values into the formula:
[tex]\[
v_{\text{max}} = \frac{2 \pi \times 5.0 \times 10^{-2}}{21}
\][/tex]
After performing the calculations, we find that:
[tex]\[
v_{\text{max}} = 0.014959965017094254 \, \text{m/s}
\][/tex]
Thus, the maximum velocity of the bob is approximately [tex]\( 0.01496 \, \text{m/s} \)[/tex].
