Question

If the frequency of a simple pendulum is $2\,Hz$ . How many oscillations will it complete in $16$ seconds?
A. $64$
B. $8$
C. $16$
D. $32$

Answer 1

In physics, frequency is the number of oscillations in one second which is inversely proportional to the time period of an oscillating body. We will find the time period of the simple pendulum and then will determine the number of oscillations in a given time.

Complete step by step answer:
Let us first understand the motion of a simple pendulum. When the bob of a pendulum starts its journey from its mean position and moves to the right extreme position and comes back to mean position then again it goes to the left extreme position and comes back to the mean position. This whole distance is covered by the simple pendulum in some time which is known as the Time period of simple pendulum and it’s called the one oscillation.
Since, $\text{frequency} = \dfrac{\text{oscillations}}{{1\sec }}$

But, we need to find the number of oscillations in $16$ seconds. So we will just put the value of one second into $16$ seconds and we will get the number of required oscillations.
Number of oscillations $= frequency \times 16\sec$
Number of oscillations $= 2 \times 16$
Number of oscillations $= 32$
So, the number of oscillations by a simple pendulum is $32$.

Hence, the correct option is D.

Note: Remember, the SI unit for frequency is $Hertz$ denoted as $Hz$ which is equivalent to ${\sec ^{ - 1}}$.And the number of oscillations simply represents how many times an oscillating body completes its forth and back movements in a given time. And its measurement is represented by frequency.