Question

A 20g particle moves in SHM with a frequency of $3$ oscillation per second and the amplitude of the $5cm$. The total distance does the particle moves during one oscillation is
(A)$10cm$
(B)$15cm$
(C)$20cm$
(D)$25cm$

Answer 1

In this question, it is given that the particle is moving in Simple harmonic motion. The simple harmonic motion of an object or particle is a forth and back movement through its equilibrium position. By using the formula angular velocity of simple harmonic motion and given values the following question can be evaluated.

Complete answer:
Given that the amplitude of the particle is $5cm$ and it is performing $3$ oscillations per second having mass $20g$.
$\Rightarrow \omega = \dfrac{{2\pi }}{T}$ ----------- $(1)$
Where $T$ is the time-period and frequency $(f)$is inverse of the time period $(T)$ which can be given as,
$\Rightarrow f = \dfrac{1}{T}$
$\Rightarrow T = \dfrac{1}{f}$
Given the particle is performing $3$ oscillations per second and as the frequency is defined as the number of oscillations per unit of time. Therefore the frequency $(f)$ will be $3Hz$ .
Substituting the value of $T$ in equation $(1)$
$\Rightarrow \omega = 2\pi f$
$\Rightarrow \omega = 2\pi \times 3 = 6\pi$
Hence the particle has an angular velocity of $6\pi \dfrac{{rad}}{\operatorname{s} }$that means in one complete oscillation particle moves from mean position to one extreme and then comes back it mean position then comes to the another extreme and then to the mean that means it covers a total of 4 times the amplitude and total distance $(d)$can be given as,
$\Rightarrow d = 4A$
Now substituting the value of amplitude provided
$\Rightarrow d = 4 \times 5cm$
$\Rightarrow d = 20cm$
Therefore the total distance covered by the particle having $20g$ mass and with amplitude $5cm$ is $d = 20cm$.

Hence the option (C) is the correct answer.

Note:
Such types of questions are a little tricky as there are many quantities given that are not useful in the calculation. For example, the mass of the particle provided is not required for the calculation. So one must be aware of the concepts and proper formula to evaluate such types of questions.