Question

10. A simple pendulum takes 90 s to complete 30 oscillations. What is the time period and frequency of the pendulum?​

Answer 1

Answer:

Frequency, i.e., per second. Hence, the pendulum oscillates 3 times in 1sec. [90/30].

what is frequency?

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. Frequency is measured in hertz which is equal to one event per second.

Answer 2

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• A simple pendulum takes 90 s to complete 30 oscillations. What is the time period and frequency of the pendulum?​

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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 :

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

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,

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

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 .