# Simple harmonic motion problems

by ilovephysics
Tags: harmonic, motion, simple
 P: 1,780 Simple harmonic motion problems Thats what it is. A pendulum, a block on a spring, two blocks with a spring mediating the forces are all examples of Simple Harmonic Oscillators for small displacements obeying Hooke's Law (which states that the restoring force is proportional to the displacement). SHM means Simple Harmonic Motion, which is the motion that a simple harmonic oscillator performs under these conditions. You need to apply the same fundamental ideas for all problems where SHM takes place. In general a motion may be oscillatory BUT NOT Simple Harmonic. This is usually when Hooke's Law breaks down or is not applicable to start with. This generally happens when the amplitude of motion is large and so the restoring force and displacement of the body performing SHM are no longer linearly related (simply put something like $F = -kx$ doesn't hold). If you noticed, SHM is governed by equations of the form [tex]\ddot{r} + \omega_{0}^2r = 0[/itex] This is a ordinary second order linear differential equation with constant coefficients (if the terminology confuses you, ignore it for now). For more complicated motions where a form of Hooke's Law does not hold, the differential equations of motion are not so simple to solve and sometimes only approximate solutions can be found. In general therefore, you cannot solve them by hand as easily as you can solve SHM equations. All you can do is set up the equations of motion using the same principles. Solving them may not be always possible. Hope that helps. Cheers Vivek