Question

A pendulum completes 60 oscillations in 5 seconds. Calculate its time period and frequency?

Answer 1

SOLUTION

GIVEN

A pendulum completes 60 oscillations in 5 seconds.

TO DETERMINE

Calculate its time period and frequency

EVALUATION

Here it is given that a pendulum completes 60 oscillations in 5 seconds

So 1 oscillation occurs in

$= \displaystyle \sf{ \frac{5}{60} \: \: \: sec}$

$= \displaystyle \sf{ \frac{1}{12} \: \: \: sec}$

Hence time period

$= \displaystyle \sf{ \frac{1}{12} \: \: \: sec}$

Now frequency

$= \displaystyle \sf{ \frac{1}{Time \: period } \: \: \: }$

$= \displaystyle \sf{ \frac{1}{ \frac{1}{12} } \: \: \:Hz }$

$= \displaystyle \sf{ 12 \: \: \:Hz }$

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Answer 2

Given :

• Number of oscillations (N) = 60

• Time taken to complete 60 oscillations (t) = 5 seconds

To find : Frequency (f) and Time period (T)

Step-by-step explanation:

• The pendulum completes 60 oscillations in 5 seconds.  So, in 1 second,

        it completes  $\frac{60}{5} = 12$ oscillations.

• So, frequency (f) = 12  Hertz

• (Since, frequency of oscillations is the number of oscillations performed by the particle in one second.)

• Time period =  $\frac{1}{Frequency} = \frac{1}{12}$ =  0.083 seconds.

• Time period is the time needed by the particle to complete one oscillation.

Answer:

Hence, Time period is 0.083 seconds and Frequency is 12 Hertz.