The more complicated (but realistic) oscillations that occur in more than one dimension are covered in Section 3, where the superposition of SHMs is discussed. The simple mechanics of SHM (along with a mathematical model of SHM and its phasor representation) are discussed in Section 2. For this reason SHM can be regarded as a basic building block of far more complicated periodic motions. In practice, when most stable systems are displaced slightly from equilibrium and then released, the periodic motion that follows can be treated as SHM, a combination of SHMs, or at least an approximation to one or more SHMs. The force has a magnitude which is proportional to the distance between the object and the position of The force is always directed towards the position of equilibrium SHM arises whenever an object is made to oscillate about a position of equilibrium by a force that has the following characteristics: In SHM the displacement, velocity and acceleration of the oscillating object can all be represented as sinusoidal functions of time. This module is concerned with one of the simplest types of periodic motion – simple harmonic motion (SHM). Such motions are described as periodic motions and the shortest time over which the motion repeats is called the period or periodic time. A common feature of many of these vibrations or oscillations is that the motion is repetitive or periodic. Vibrations range from the small–scale motions of atoms in solids to the large–scale swaying of bridges and tall buildings from the irregular bending of a tree in the wind to the extremely regular oscillations of the balance wheel of a watch. Others, such as the vibrations caused by machinery and traffic, are noisy and annoying.
Some are very welcome and aesthetically pleasing, such as the vibrations of musical instruments. Within minutes of waking up, you may well experience vibrations in a wide variety of forms: the buzzing of the alarm clock the bounce of your bed the oscillations of a loudspeaker, which in turn are produced by oscillations of charges in electric circuits the vibrations of an electric toothbrush or an electric razor, and so on. Vibrations and oscillations are part of your everyday life.