Question

An oscillator completes 240 cycles in 5.2 minutes.

Calculate its period (in seconds) and frequency (in Hz).

Answer 1

I. Period = 1.3 seconds

II. Frequency = 0.769 Hertz

Step-by-step explanation:

Given the following data;

Number of oscillation = 240 cycles

Time = 5.2 minutes.

Conversion:

1 minute = 60 seconds

5.2 minutes = X seconds

X = 60 * 5.2

X = 312 seconds

To find the following;

I. Period

Mathematically, the number of oscillation of a pendulum is given by the formula;

`Number \; of \; oscillation = \frac {Time}{Period}`

Making period the subject of formula, we have;

`Period = \frac {Time}{Number \; of \; oscillation}`

Substituting into the formula, we have;

`Period = \frac {312}{240}`

Period = 1.3 seconds

II. Frequency

`Frequency = \frac {1}{Period}`

Substituting the values into the formula, we have;

`Frequency = \frac {1}{1.3}`

Frequency = 0.769 Hertz