ABSTRACT
We shall now study a few versions of the simple system called ‘the harmonic oscillator’. First we will analyse the behaviour of a vibrating string via a simplified model, in which we place a metal ball in the middle of the string. See fig.3.1.1. Thanks to this ball we can ignore the mass of the string itself, which simplifies the calculation considerably. On the ball in both directions a force S is exercised by means of the tension of the string. We now assume now that during the vibration the displacement and therefore the changes in the length of the string are so small that we may consider S as a constant. We indicate the displacement of the ball with y(t). If the string at the place of the ball is pulled to the side the two forces S no longer lie in each others direction and a restoring force F occurs, which is shown in the diagram via the parallelogram construction and can be calculated as follows: https://www.w3.org/1998/Math/MathML"> F = 2 S ’ = 2 S sin α ≈ 2 S α https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203059487/f82eba0c-3784-4bb3-9b99-68db5a0007a1/content/inline-math_61_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
