Question

A simple pendulum takes 90 seconds to complete 30 oscillations. What is the time period and frequency of the pendulum?
please answer

Answer 1

Answer :-

→ Time period is 3 seconds .

→ Frequency is 0.33 Hz .

Explanation :-

We have :-

→ Time taken = 90 sec

→ Oscillations in given time = 30

________________________________

We know that, time period of a pendulum is the time taken to complete 1 oscillation.

Thus, time period :-

⇒ T = 90/30

⇒ T = 3 sec

________________________________

Now, we have :-

T = 1/f

Where :-

• T is time period.

• f is frequency.

Substituting values, we get :-

⇒ 3 = 1/f

⇒ 3f = 1

⇒ f = 1/3

⇒ f = 0.33 Hz

Answer 2

Answer:

Given :-

• A simple pendulum takes 90 seconds to complete 30 oscillations.

To Find :-

• What is the time period and frequency of the pendulum.

Formula Used :-

$\clubsuit$ Time Period Formula :

$\longmapsto \sf\boxed{\bold{\pink{Time\: Period =\: \dfrac{1}{Frequency}}}}$

Solution :-

First, we have to find the time period of the pendulum :

$\mapsto$ A body makes 90 seconds to complete 30 oscillations. Then time taken to complete 1 oscillations :

Given :

$\bigstar$ Total time taken = 90 seconds

$\bigstar$ Number of Oscillations = 30 oscillations

According to the question by using the formula we get,

$\implies \sf Time\: Period =\: \dfrac{9\cancel{0}}{3\cancel{0}}$

$\implies \sf Time\: Period =\: \dfrac{\cancel{9}}{\cancel{3}}$

$\implies \sf Time\: Period =\: \dfrac{3}{1}$

$\implies \sf\bold{\red{Time\: Period =\: 3\: seconds}}$

$\therefore$ The time period of the pendulum is 3 seconds.

Now, we have to find the frequency of the pendulum:

Then,

$\longmapsto \sf\bold{\green{Frequency =\: \dfrac{1}{Time\: Period}}}$

Given :

$\bigstar$ Time Period = 3 seconds

According to the question by using the formula we get,

$\longrightarrow \sf Frequency =\: \dfrac{1}{3}$

$\longrightarrow \sf\bold{\red{Frequency =\: 0.33\: Hz}}$

$\therefore$ The frequency of the pendulum is 0.33 Hz .