The displacement 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:

Option 1 - 6 s

Option 2 - 8 s

Option 3 - 12 s

Option 4 - 36 s

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 4

Detailed Solution:

$x = A s i n ω t$

Angle travelled by while moving from A to B

$θ = 30 ° = \frac{π °}{6}$

$θ = ω t$

$\frac{π}{6} = ω * 3 [t = 3 s e c]$

$ω = \frac{π}{18}$

$\Rightarrow T = \frac{2 π}{ω} = \frac{2 π * 18}{π} = 36 s e c$

T = 36 sec

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