To find the frequency of a spring that is oscillating, we can use the relationship between the period and the frequency of an oscillating object. The period (T) is the time it takes for one complete cycle of oscillation, and the frequency (f) is the number of cycles per second.
The formula that relates the period (T) to the frequency (f) is given by:
[tex]\[ f = \frac{1}{T} \][/tex]
Where:
- [tex]\( T \)[/tex] is the period in seconds
- [tex]\( f \)[/tex] is the frequency in Hertz (Hz)
Given:
- The period [tex]\( T = 0.228 \)[/tex] seconds
Substitute the given period into the formula to find the frequency:
[tex]\[ f = \frac{1}{0.228} \][/tex]
When you perform the calculation, you find:
[tex]\[ f \approx 4.385964912280701 \ \text{Hz} \][/tex]
Thus, the frequency of the spring's oscillation is approximately 4.39 Hz.
