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Question 10

A particle executes simple harmonic motion between $$x = -A$$ and $$x = +A$$. If time taken by particle to go from $$x = 0$$ to $$\frac{A}{2}$$ is 2 s; then time taken by particle in going from $$x = \frac{A}{2}$$ to $$A$$ is:

Solution

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Solution :

For SHM,

x = A sin(ωt)

Given that particle goes from

x = 0 to x = A/2 in 2 s

So,

A sin(ωt) = A/2

⇒ sin(ωt) = 1/2

⇒ ωt = π/6

Thus,

t = π/(6ω) = 2 s

Now, time taken from x = A/2 to x = A :

At x = A/2,

ωt₁ = π/6

At x = A,

ωt₂ = π/2

Therefore,

Δt = (π/2ω) − (π/6ω)

= π/(3ω)

But,

π/(6ω) = 2 s

Hence,

π/(3ω) = 4 s

Final Answer :

2 s

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