Question

A particle executing SHM completes $120\pi$ vibrations in one minute. What is the frequency of this motion?
A. $5Hz$
B. $2\pi Hz$
C. $1Hz$
D. None of these

Answer 1

We start by noting down the given information and formulas relating to them. We then convert minutes to seconds and use the cross multiplication method to find the value in one second. We do this because the frequency is the number of vibrations made in a second.

Formulas used:
Frequency can be found out using the formula,
$f = \dfrac{1}{T}$
where, $T$ is the time period.

Complete step by step answer:
We know that the frequency is the number of cycles per second.
One minute is sixty seconds, $1\min = 60s$
It is given that, the particle completes $120\pi$ vibrations in one minute, to find the number of vibrations in one second, we use cross multiplication,
$120\pi = 60s$
$\Rightarrow x = 1s$
The value of $x$ can be found by cross multiplication method,
$x = \dfrac{{1 \times 120\pi }}{{60}} = 2\pi Hz$
We defined frequency as the number of vibrations (in this case) made in one second.
Hence the frequency of the motion is, $2\pi Hz$

Therefore, the right answer is option B.

Note: Frequency, as the name suggests, is the measure of how frequent an instance occurs, in other words, it is the measure of occurrences of a repeating event over time. It is also defined as the reciprocal of the time period (time period is the time taken for one complete cycle of vibration to pass one point). The conversion of minutes to seconds must be done so as to avoid miscalculations leading to wrong answers. Frequency is defined in seconds, hence the answer also has to be in seconds inverse.