Complex harmonic motion

In physics, complex harmonic motion is a complicated realm based on the simple harmonic motion. The word "complex" refers to different situations. Unlike simple harmonic motion, which is regardless of air resistance, friction, etc., complex harmonic motion often has additional forces to dissipate the initial energy and lessen the speed and amplitude of an oscillation until the energy of the system is totally drained and the system comes to rest at its equilibrium point.

Damped harmonic motion is a real oscillation, in which an object is hanging on a spring. Because of the existence of internal friction and air resistance, the system will over time experience a decrease in amplitude. The decrease of amplitude is due to the fact that the energy goes into thermal energy.

Damped harmonic motion happens because the spring is not very efficient at storing and releasing energy so that the energy dies out. The damping force is proportional to the velocity of the object and is at the opposite direction of the motion so that the object slows down quickly. Specifically, When an object is damping, the damping force will relate to velocity with a coefficient c. The equation is "F=-cv".

The diagram shown on the right indicates three types of damped harmonic motion.

An object or a system is oscillating in its own natural frequency without the interference of an external periodical force or initial motion. Damped oscillation is similar to forced oscillation except that it has continuous and repeated force as it is going. Hence, these are two motion that has opposite result.

free oscillator and the damping effects of air resistance and losses at the pivots mean it will eventually stop swinging. If the swing is pushed each time it reaches a certain point it behaves as a forced oscillator and will continue to swing for as long as energy is supplied.

Resonance occurs when the frequency of the external force (applied) is the same as the natural frequency (resonant frequency) of the system. When such a situation occurs, the external force always acts in the same direction as the motion of the oscillating object, with the result that the amplitude of the oscillation increases indefinitely, as it's shown in the diagram on the right. Away from the value of resonant frequency, either greater or lesser, the amplitude of the corresponding frequency is smaller.

In a set of driving pendulums with different length of strings hanging objects, the one pendulum with the same length of string as the driver gets the biggest amplitude of swinging.

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