A pendulum is executing simple harmonic motion and its maximum kinetic energy is K 1 . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in t

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A pendulum is executing simple harmonic motion and its maximum kinetic energy is K 1 ​ . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K 2 ​

TestHub · Accepted Answer

K = 2 1 ​ m ω 2 x 2 ⇒ K m a x ​ = 2 1 ​ m ω 2 A 2 A = L θ ω = L g ​ ​ ⇒ K = 2 1 ​ m ⋅ L g ​ ⋅ L 2 θ 2 = 2 1 ​ m gL θ 2 ∴ K 2 ​ K 1 ​ ​ = 2 L L ​ = 2 1 ​ ⇒ K 2 ​ = 2 K 1 ​ ∴ K 2 ​ K 1 ​ ​ = 2 L L ​ = 2 1 ​ ⇒ K 2 ​ = 2 K 1 ​

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