Find the displacement of a simple harmonic oscillator at which its P.E. is half of the maximum energy of the oscillator.

Explanation

Let at an instatn the displacement of the particle from the mean position be y. Then its PE is
`E_(P)=(1)/(2)momega^(2)y^(2)`
Total energy, `E=(1)/(2)momega^(2)r^(2)`
As per question, `PE=(1)/(2)xxTE`
`:.(1)/(2)momega^(2)y^(2)=(1)/(2)xx(1)/(2)momega^(2)r^(2) or y^(2)=(r^(2))/(2) or y=+-(r)/(sqrt(2))`