Answer:
Period of this oscillation: approximately [tex]2.2\; {\rm s}[/tex].
Frequency of this oscillation: approximately [tex]0.45\; {\rm Hz}[/tex].
Explanation:
Time period is the duration of each cycle. The unit of period is the same as the unit of time: seconds.
In this example, [tex]200[/tex] cycles requires [tex]89\; {\rm s}[/tex] to complete, so each cycle would have taken:
[tex]\begin{aligned}T = \frac{200\; {\rm s}}{89} \approx 2.2\; {\rm s}\end{aligned}[/tex].
Frequency is the number of cycles completed in each unit time (e.g., in [tex]1\; {\rm s}[/tex].) The unit of frequency is the reciprocal of the unit of time (i.e., one over the unit of time, [tex]{\rm s^{-1}}[/tex].) Note that [tex]1\; {\rm s^{-1}} = 1\; {\rm Hz}[/tex].
In this example, there are [tex]200[/tex] cycles in [tex]89\; {\rm s}[/tex], so there would be [tex](200 / 89)[/tex] cycles in every [tex]1\; {\rm s}[/tex]. Hence, the frequency of this pendulum will be:
[tex]\begin{aligned}f = \frac{89}{200\; {\rm s}} \approx 0.45\; {\rm s^{-1}} = 0.45\; {\rm Hz}\end{aligned}[/tex].
