University of St Andrews
School of Physics and Astronomy

6.  Oscillations

Return to the First Year Waves and Optics Home Page
Associated tutorial questions (St Andrews only)

• Oscillations, and simple harmonic motion ideas
• Use mechanics (Newton F = ma and Hooke F = - kx) to derive for mass on a spring     m d²x/dt² = - (k/m) x
• Show that a solution to the above equation of motion is x = A cos(wt + W)  with  w² = k/m
• Phase of an oscillation - the part in the brackets of the cosine term, which we will usually measure in radians (not degrees)
• Period of an oscillation shown to be T = 2 pi / w  = 1/f
• Position, velocity, and acceleration - how are they related (v = dx/dt etc), what are the phase shifts, how do they depend on w and A?
• Comments on systems that are approximately simple harmonic, including the small-angle pendulum, where by using mechanics we find w² = g/l

Note: we expect you to have memorised Newton's second law and Hooke's law.  I do not expect you to remember the oscillation frequency of a pendulum or mass on a spring - you should now readily be able to work it out in the way we did in lectures, starting from the idea of a "trial" solution of the form A cos(wt).   Being able to do these "derivations" reduces how much you need to learn parrot-fashion, gives you a better understanding of the science, gives you a better idea about what systems can sensibly be described by this mathematics, and gives you practice in techniques of mathematics in physics that you will be applying more generally later.

Similar material to that presented in the lectures is available at:-

• Halliday, Resnick, & Walker - Chapters on:-  Oscillations

Associated tutorial questions (St Andrews only)
Return to Waves and Optics Home Page

Created by, and copyright of, Bruce Sinclair, University of St Andrews; last modified 11/09/01