Periodic Motion 

Frequency 

Frequency is the number of occurrences of a repeating event per unit time.

Period

The time taken for one full oscillation, it is the reciprocal of frequency

Angular Frequency

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector \vec{\omega} is sometimes used as a synonym for the vector quantity angular velocity.

Centripetal Force

Centripetal force is a force that makes a body follow a curved path: its direction is always orthogonal to the velocity of the body, toward the fixed point of the instantaneous center of curvature of the path. Centripetal force is generally the cause of circular motion.

Simple Harmonic Motion

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. It can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration. Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency.

Restoritive Force 

Restorative force is a force which helps the body to its original position i.e. its mean position.It always acts in the direction opposite to the applied force in a body.The best example for this is the spring-block system.

Damped Harmonic Motion

In physics damping is an effect that reduces the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator. This effect is linearly related to the velocity of the oscillations.

Under damped 

An under-damped is a situation, the system will oscillate at the natural damped frequency ω, which is a function of the natural frequency and the damping ratio. To continue the analogy, an Underdamped door closer would close quickly, but would hit the door frame with significant velocity, or would oscillate in the case of a swinging door.

Critically damped

  A critically damped system converges to zero as fast as possible without oscillating. An example of critical damping is the door closer seen on many hinged doors in public buildings. The recoil mechanisms in most guns are also critically damped so that they return to their original position, after the recoil due to firing, in the least possible time.

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Over damped

An over-damped door-closer will take longer to close than a critically damped door would.

Driven Harmonic Motion

 Also known as forced harmonic motion, this is harmonic motion in which the system is given a periodic push. A perfect example is a person on a swing.

How the system behaves depends on how the frequency of the driving force compares to the natural frequency of oscillation of the system.

Definition Provided by Boston University 

Resonance

Resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies, or resonance frequencies. At these frequencies, even small periodic driving forces can produce large amplitude oscillations, because the system stores vibrational energy.