W denotes to the total energy of a particle in linear S.H.M. At a point, equidistant from the men position and extremity of the path of the particle

Options

A. K.E. of the particle will be w/2 and P.E. will also be w/2
B. K.E. of the particle will be w/4 and P.E. will be 3 w/4
C. K.E. of the particle will be 3w/4 and P.E. will be w/4
D. K.E. of the particle will be w/8 and P.E. will be 7 w/8

Answer

C

Explanation

`KE=(1)/(2)momega^(2)(A^(2)-x^(2))atx=(A)/(2)`
`=(1)/(2)momega^(2)(A^(2)-(A^(2))/(4))`
`=(1)/(2)momega^(2)A^(2)xx(3)/(4)=(3)/(4)W`
`PE=(1)/(2)mw^(2)(A^(2))/(4)=(1)/(4)W`.