For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement ' x ' from the mean position. If ' A ' is the amplitude of S.H.M the val

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For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement ' x ' from the mean position. If ' A ' is the amplitude of S.H.M the value of ' x ' is

TestHub · Accepted Answer

Potential energy: U = 2 1 ​ m ω 2 x 2 and Kinetic energy: K = 2 1 ​ m ω 2 ( A 2 − x 2 ) Given: Potential energy = 8 × Kinetic energy ​ U = 8 K 2 1 ​ m ω 2 x 2 = 8 × 2 1 ​ m ω 2 ( A 2 − x 2 ) x 2 = 8 A 2 − 8 x 2 9 x 2 = 8 A 2 x 2 = 9 8 A 2 ​ x = 3 2 2 ​ A ​ ​

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