When the displacement of a particle executing SHM is one-fourth of its amplitude, what fraction of the total energy is the kinetic energy?

Options

A. `(3)/(4)`
B. `(2)/(3)`
C. `(1)/(2)`
D. `(2)/(5)`

Answer

A

Explanation

`x=(A)/(2) and v= omegasqrt(A^(2)-x^(2))`
`therefore E_(K)=(1)/(2)mv^(2)=(1)/(2)m omega^(2)(A^(2)-(A^(2))/(4))`
`=(3)/(8)m omega^(2)A^(2)`
`therefore (E_(K))/(E_(T))=((3)/(8)momega^(2)A^(2))/((1)/(2)momega^(2)A^(2))=(3)/(4)`