Oscillations occur whenever a force exists that pushes an object back towards a stable equilibrium position whenever it is displaced from it.
Such forces abound in nature - things are held together in structured form because they are in stable equilibrium positions and when they are disturbed in certain ways, they oscillate.
When the displacement from equilibrium is small, the restoring force is often linearly related to the displacement, at least to a good approximation. In that case the oscillations take on a special character - they are called harmonic oscillations as they are described by harmonic functions (sines and cosines) known from trigonometery.
In this course we will study simple harmonic oscillators, both with and without damping forces. The principle examples we will study will be masses on springs and various penduli.
Springs obey Hooke's Law:
(where 
is called
the spring constant. A perfect spring produces perfect harmonic
oscillation, so this will be our archetype.
A pendulum (as we shall see) has a restoring force or torque proportional to displacement for small displacements but is much too complicated to treat in this course for large displacements. It is a simple example of a problem that oscillates harmonically for small displacements but not harmonically for large ones.
An oscillator can be damped by dissipative forces such as friction and viscous drag. A damped oscillator can have exhibit a variety of behaviors depending on the relative strength and form of the damping force, but for one special form it can be easily described.