What should be the displacement of a particle, executing SHM, from its position of equilibrium so that the kinetic energy of the particle is half of its maximum kinetic energy?

Explanation

Maximum kinetic energy of a particle executing SHM = `1/2momega^(2)A^(2)`
When the displacement of the particle is x from the position of equilibrium, kinetic energy of the particle = `1/2momega^(2)(A^(2)-x^(2))`
According to the question,
`1/2momega^(2)(A^(2)-x^(2))=1/2xx1/2momega^(2)A^(2)`
or, `A^(2)-x^(2)=A^(2)/2`
or, `x^(2)=A^(2)-A^(2)/2=A^(2)/2`
or, `x=pmA/sqrt2`, this is the required displacement.