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A particle performs simple harmonic motion with a period of 2 seconds. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is `1/a` s. The value of 'a' to the nearest integer is ______.

#### Options

6

5

4

2

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#### Solution

A particle performs simple harmonic motion with a period of 2 seconds. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is `1/a` s. The value of 'a' to the nearest integer is **6.**

**Explanation:**

From Y = A sinωt

⇒ `A/2 = Asin((2pit)/T)` [∵ Y = `A/2` from question]

⇒ `sin((2pit)/T) = A/(2 xx A) = 1/2 ⇒ (2pit)/T = pi/6`

⇒ t = `T/12 = 2/12 = 1/6` seconds

∴ a = 6

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