An object of mass `0.2 kg` executes simple harmonic oscillation along the `x - axis`with a frequency of `(25//pi) Hz`. At the position `x = 0.04`, the object has Kinetic energy of `0.5 J` and potential energy `0.4 J. The amplitude of oscillations is……m.

Explanation

`U = (1)/(2) m omega^(2) x^(2) = (1)/(2) xx 0.2 xx 50^(2) xx 16 xx 10^(-4) = 0.4 J`
Total energy of oscillation is `(0.5 + 0.4) = 0.9J`
`:. 0.9 = (1)/(2) KA^(2) (or) A = sqrt((1.8)/(K)) = sqrt(1.8)/(m omega^(2))`
`A = (1)/(omega) sqrt((1.8)/(0.2)) = 0.06 m`