The linear displacement 'x' of the bob of simple pendulum from its mean position varies as x = a sin ( 2 π t ) where 'a' is its amplitude expressed in metre and 't' i

Question

The linear displacement 'x' of the bob of simple pendulum from its mean position varies as x = a sin ( 2 ​ π ​ t ) where 'a' is its amplitude expressed in metre and 't' is in second. The length of simple pendulum is (Take ' g ′ = π 2 m / s 2 )

TestHub · Accepted Answer

x = a sin ( 2 ​ π ​ t ) ∴ ω = 2 ​ π ​ = T 2 π ​ ∴ T = 2 2 ​ T = 2 π g ℓ ​ ​ 2 2 ​ = 2 π g ℓ ​ ​ 2 = π 2 g ℓ ​ ∴ ℓ = π 2 2 g ​ = 2 m

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