Oscillations - Result Question 45

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49. A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

======= ####49. A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/oscillations/oscillations—result-question-45.md (a) $T / 8$

(b) $T / 12$

(c) $T / 2$

(d) $T / 4$

[2007]

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Answer:

Correct Answer: 49. (b)

Solution:

  1. (b) Displacement from the mean position

$y=a \sin (\frac{2 \pi}{T}) t$

According to problem $y=a / 2$

$a / 2=a \sin (\frac{2 \pi}{T}) t$

$\Rightarrow \frac{\pi}{6}=(\frac{2 \pi}{T}) t \Rightarrow t=T / 12$

This is the minimum time taken by the particle to travel half of the amplitude from the equilibrium position.