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.

Options

A. 4 cm
B. 8 cm
C. 2 cm
D. 6 cm

Answer

D

Explanation

`T.E.=K.E.+P.E.`
`=0.5+0.4=0.9`
`(1)/(2)momega^(2)A^(2)=0.9`
`=A^(2)=(2xx0.9)/(m4pi^(2)n^(2))=(0.9xx2)/(0.2xx4xxpi^(2)xx(25)/(pi^(2)))`
`A^(2)=(9)/(4xx25xx25)`
`therefore A=(3)/(2xx25)=(3)/(50)=0.06m`
`A=6cm`