JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Elasticity & SHM

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The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

(A)6 s
(B)8 s
(C)12 s
(D)36 s✓ Correct

Answer: (D)

Solution

For SHM starting from mean position,

x = A sin (ω t)

. Given

x = \frac{A}{2}

t = 3

s, we have

sin (3 ω) = \frac{1}{2}

. The smallest positive solution is

3 ω = \frac{π}{6}

, giving

ω = \frac{π}{18}

. Since

ω = \frac{2 π}{T}

, we get

T = 36

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Single correct option

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