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. Types Damped harmonic motion Introduction 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 be related to velocity by a coefficient : The diagram shown on the right indicates three types of damped harmonic motion. Critically damped: The system returns to equilibrium as quickly as possible without oscillating. Underdamped: The system oscillates (at reduced frequency compared to the undamped case) with the amplitude gradually decreasing to zero. Overdamped: The system returns (exponentially decays) to equilibrium without oscillating. Difference between damped and forced oscillation An object or a system is oscillating in its own natural frequency without the interference of an external periodic force or initial motion. Damped oscillation is similar to forced oscillation except that it has continuous and repeated force. Hence, these are two motions that have opposite results. Examples Bungee jumper provides a large force of bouncing by compressing the springs underneath it. The compression theoretically turns the kinetic energy into elastic potential energy. When the elastic potential energy reaches its top boundary, it can be exerted onto the object or child that presses on it within the form of kinetic energy. Rubber band works the same as the spring. Resonance Introduction 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