Q.

A pendulum is oscillating in a vertical plane. The acceleration at the extreme position and lowest position are equal. Then the angular amplitude of the pendulum is

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a

tan−12

b

tan−12

c

tan−11/2

d

2tan−112

answer is D.

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Detailed Solution

acceleration at the extreme position gsinθ  and lowest position v2l . gsinθ=v2l From conservation of energy  12mv2=mgl1−cosθmv2l=2mg1−cosθgsinθ=2g1−cosθsinθ=4sin2θ22sinθ2cosθ2=4sin2θ2tanθ2=12θ2=tan−112θ=2tan−112
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A pendulum is oscillating in a vertical plane. The acceleration at the extreme position and lowest position are equal. Then the angular amplitude of the pendulum is