Question

A simple pendulum makes 200 oscillations in 89 seconds. What is the time period and frequency of its oscillation?​

Answer 1

Period of this oscillation: approximately
`2.2\; {\rm s}`.

Frequency of this oscillation: approximately
`0.45\; {\rm Hz}`.

Step-by-step 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,
`200` cycles requires
`89\; {\rm s}` to complete, so each cycle would have taken:

`\begin{aligned}T = \frac{200\; {\rm s}}{89} \approx 2.2\; {\rm s}\end{aligned}`.

Frequency is the number of cycles completed in each unit time (e.g., in
`1\; {\rm s}`.) The unit of frequency is the reciprocal of the unit of time (i.e., one over the unit of time,
`{\rm s^(-1)}`.) Note that
`1\; {\rm s^(-1)} = 1\; {\rm Hz}`.

In this example, there are
`200` cycles in
`89\; {\rm s}`, so there would be
`(200 / 89)` cycles in every
`1\; {\rm s}`. Hence, the frequency of this pendulum will be:

`\begin{aligned}f = \frac{89}{200\; {\rm s}} \approx 0.45\; {\rm s^(-1)} = 0.45\; {\rm Hz}\end{aligned}`.