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A simple pendulum of length $ℓ$ is tilted at an angle $α$ and imparted an initial velocity v₁towards mean position. Initial phase of bob is given as (A₁ is linear amplitude and
assume that maximum angular displacement of bob is very small)

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$π - \sin^{- 1} (\frac{ℓ α}{A_{1}})$

$π - \cos^{- 1} (\frac{ℓ α}{A_{1}})$

$\sin^{- 1} (\frac{ℓ α}{A_{1}})$

$2 π - \sin^{- 1} (\frac{ℓ α}{A_{1}})$

answer is B.

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Detailed Solution

$\begin{array}{l} In phasor diagram, \sin θ = \frac{ℓ α}{A_{1}} \\ ∴ Initial phase ϕ = 2 π - θ = 2 π - \sin^{- 1} (\frac{ℓ α}{A_{1}}) \end{array}$

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