A mass 0.4 kg performs S.H.M. with a frequency π 16 Hz . At a certain displacement it has kinetic energy 2 J and potential energy 1.2 J . The amplitude of oscillation is

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A mass 0.4 kg performs S.H.M. with a frequency π 16 ​ Hz . At a certain displacement it has kinetic energy 2 J and potential energy 1.2 J . The amplitude of oscillation is

TestHub · Accepted Answer

​ m = 0.4 kg , f = π 16 ​ Hz , K ⋅ E ⋅ = 2 J , P.E. = 1.2 J ω = 2 π f = 2 π × π 16 ​ = 32 rad / s ​ Total energy T.E. = 2 + 1.2 = 3.2 J ​ TE = 2 1 ​ m 2 A 2 ∴ A 2 = m ω 2 2 ( TE ) ​ = 0.4 × ( 32 ) 2 2 × 3.2 ​ = 0.4 × ( 32 ) 2 6.4 ​ = ( 32 ) 2 16 ​ ∴ A = 32 4 ​ = 8 1 ​ = 0.125 m ​

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