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

Find the displacement of a simple harmonic oscillator at which its PE

1.	Find the displacement of a simple harmonic oscillator at which its PE is half of the maximum energy of the oscillator.
Answer» Solution :If the amplitude of oscillator is A and DISPLACEMENT x at time t, then TOTAL energy `E= (1)/(2) kA^(2)` and Potential energy `U= (1)/(2) kx^(2)` but potential energy `PE= (1)/(2) E` is given, `THEREFORE (1)/(2) kx^(2)= (1)/(2)xx (1)/(2) kA^(2)` `therefore x^(2)= (A^2)/(2)` `therefore x= pm (A)/(sqrt(2))`. Sign `pm` indicates that oscillator will be in one side from mean position.