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Q.

A simple pendulum of length ℓ is tilted at an angle α and imparted an initial velocity v1 towards mean position. Initial phase of bob is given as (A1 is linear amplitude andassume that maximum angular displacement of bob is very small)

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a

sin−1⁡ℓαA1

b

2π−sin−1⁡ℓαA1

c

π−sin−1⁡ℓαA1

d

π−cos−1⁡ℓαA1

answer is B.

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Detailed Solution

In phasor diagram, sin⁡θ=ℓαA1∴ Initial phase ϕ=2π−θ=2π−sin−1⁡ℓαA1
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