Theory And Examples Of Simple Harmonic Motion

Description
An example of S.H.M is the motion of a liquid in an U-tube. The equation of motion for such a liquid is derived using conservation of energy which is different from most of the text books where second law of motion is used.A torsional pendulum behaves much like a one dimensional spring--time period does not depend on amplitude for small disturbance.Equation of motion of a torsional pendulum is derived here.An experiment to measure the time period and also to show the similarity of behaviour of a torsional pendulum and spring. It shows that just like a spring which is permanently damaged if stretched by a large amplitude a torsional pendulum also can be given a twist so large so as to deform the suspension wire. Equation of motion for an oscillating object of arbitrary shape is derived. Time period for the same is calculated and shown to be independent of mass. Here objects of regular geometrical shapes like rod, bob, disc etc are considered and their time period is calculated and experimentally verified.The interesting part is that all these objects were made in such a way that they had same time period. . This gives a rare insight to the whole problem.

Prof. Walter Lewin, 8.01 Physics I: Classical Mechanics, Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed June 14, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc