Question

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

Answer 1

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))`