Question

If a simple pendulum makes 20 oscillations in 4 seconds, what is the frequency?

Answer 1

To do this question we have to use the formula of frequency that is $f=\dfrac{1}{T}$. And have the knowledge of unitary methods. Before moving ahead let's talk about what a unitary method is. Suppose we went to the market and bought $2$mangoes for rupees $10$. So what is the price of $5$mangoes.
2 mangoes = $10$rupees
1 mango = $\dfrac{10}{2}=5$ rupees
5 mangoes =$5\times 5=25$rupees

Complete step by step answer:
Simple pendulum: It is fixed with a rigid body and has some mass attached to its string and oscillates into and fro motion.
Oscillation: when one complete to and fro motion is completed by oscillating bodies then it is called oscillation.
Frequency: Number of oscillation per second is called frequency. It's S.I. unit is hertz.
Time period: time taken to complete one oscillation is called its time period.

Now let us calculate the frequency when pendulum makes 20 oscillation in 4 seconds,
20 oscillation = 4 seconds
1 oscillation = $\dfrac{4}{20}=\dfrac{1}{5}\sec$
So, for single oscillation $\dfrac{1}{5}\sec$ is taken. so time period of the pendulum $\dfrac{1}{5}\sec$.
$\Rightarrow f=\dfrac{1}{T}$
$\therefore f=5\,Hz$

Hence, the frequency is 5 Hz.

Note: If we immerse a simple pendulum in water then it will experience a buoyant force in upward direction. In addition to the other force like gravity and tension.In simple pendulum , we can find the value of equivalent force constant of oscillation ${{k}_{eq}}$=$\dfrac{T}{l}$ ; where $T$ is the tension in the string at equilibrium position of the bob and O is the length of the string.