Question

The equation of motion of a particle of mass 1 g is where x is displacement (in m) from mean position. Find out the frequency of oscillation ( in Hz)-
(A) $\dfrac{1}{2}$
(B) ${2}$
(C) ${5}\sqrt{10}$
(D) $\dfrac{1}{5\sqrt{10}}$

Answer 1

Hint
Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

Complete step by step answer
According to motional formula of acceleration $a = - {\omega ^2}x$ … (1)
The given equation is,
$\dfrac{{{d^2}x}}{{d{t^2}}} + {\pi ^2}x = 0$
$\Rightarrow \dfrac{{{d^2}x}}{{d{t^2}}} = - {\pi ^2}x$ … (2)
Now, comparing equation 2 with equation 1
We get, $a = \dfrac{{{d^2}x}}{{d{t^2}}}$ , $\omega = \pi$
We know the value of ω is = 2πf
Now putting the value of omega in the relation we get,
$\begin{gathered} 2\pi f = \pi \\\ \therefore f = \dfrac{1}{2} \\\ \end{gathered}$
So, the frequency of oscillation is $f = \dfrac{1}{2}$ Hz.
Option (A) is correct.

Note
Frequency describes the number of waves that pass a fixed place in a given amount of time. So if the time it takes for a wave to pass is 1/2 second, the frequency is 2 per second. The hertz measurement, abbreviated Hz, is the number of waves that pass by per second.