Question

A simple pendulum takes 80s to complete 20 oscillations . What is the time period of the pendulum

Answer 1

Answer :

➥ The time period of the pendulum = 4 sec

Given :

➤ A simple pendulum takes 80 sec to complete 20 oscillations.

To Find :

➤ Time period of the pendulum = ?

Required Solution :

To find the time period of the pendulum, first we need to find the frequency of the pendulum It is equal to number of oscillations per second. After that we will find the time period of the pendulum.

We can find the frequency of the pendulum, by using the formula which says frequency = oscillations/time taken.

☁️ So let's calculate frequency !

As we know that

$\tt{\hookrightarrow Frequency = \dfrac{Oscillations}{Time \: taken}}$

$\tt{\hookrightarrow Frequency = \dfrac{2 \cancel{0}}{8 \cancel{0}}}$

$\tt{\hookrightarrow Frequency = \cancel{\dfrac{2}{8} }}$

$\bf{\hookrightarrow \underline{ \: \: \underline{ \orange{ \: \: Frequency = 0.25 \: H z \: \: }} \: \: }}$

Now, we have frequency of the pendulum,

• Frequency of the pendulum (F) = 0.25 H z

☃️ So let's find the time period of the pendulum by using the formula:

As we know that

$\tt{:\implies Time \: period =\dfrac{1}{Frequency}}$

$\tt{:\implies Time \: period = \cancel{\dfrac{1}{0.25}}}$

$\bf{:\implies \underline{ \: \: \underline{ \red{ \: \: Time \: period = 4 \: sec \: \: }} \: \: }}$

║Hence, the time period of the pendulum is 4 sec.║