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

PE of oscillator, U = \(\frac{1}{2}mw^2y^2\)  

{y = displacement Maximum – energy of oscillator, E = \(\frac{1}{2}mw^2A^2\)}

U = \(\frac{1}{2}E\)

or \(\frac{1}{2}mw^2y^2\) = \(\frac{1}{2}mw^2A^2\)

or y² = \(\frac{A^2}{2}\)

or y = \(\pm\frac{A}{\sqrt 2}\)