What is the difference between
1. free vibration
2. forced vibration
3. damped vibration &
4. forced damped vibration
How do their frequency, amplitude and energy change with respect to time and displacement?
What are the differences between
1. umdamped vibration
2. lightly damped vibration
3. heavily damped vibration
4. critically damped vibration &
5. over damped vibration ?
Free vibration is a vibration in which energy is neither added to nor removed from the vibrating system. It will just keep vibrating forever at the same amplitude. Except from some superconducting electronic oscillators, or possibly the motion of an electron in its orbit about an atomic nucleus, there are no free vibrations in nature. They are all damped to some extent.
Damped vibration is one in which there is an energy loss from the vibrating system. This loss may be in the form of mechanical friction, as at the pivot of a pendulum for example, or in the form of turbulence as the vibrating system distrubs its surroundings. The amplitude of a damped vibration will eventually decay to zero.
Forced vibration is one in which energy is added to the vibrating system, as for example in a clockwork mechanism where the energy stored in a spring is transferred a bit at a time to the vibrating element. The amplitude of a forced, undamped vibration would increase over time until the mechanism was destroyed. The amplitude of a forced, damped vibration will settle to some value where the energy loss per cycle is exactly balanced by the energy gained.
The amplitude changes are described above. The energy of a vibrating system is related to the amplitude. More amplitude, more energy. The frequency of a vibrating system depends on whether it is forced or not. A forced vibration may be made to assume the frequency of the forcing function. Unforced vibrations occur at a natural frequency dependent on the characteristics of the vibrating system. Basically the natural frequency of a vibrating system increases with the stiffness of the elements and decreases with their mass. Strictly speaking the frequency of a vibrator is only defined if the amplitude is constant. If the amplitude is changing the waveform contains an infinite series of frequencies.
Undamped vibration suffers no energy loss. Lightly damped vibrations have slight energy loss which may or may not be negligible, depending on the nature of the observation of the vibrator. The inertial forces in these systems are large compared to the drag or friction forces. Heavily damped vibrations suffer high energy losses. They are characterized by drag or friction forces large compared to the inertial forces of the system. A critically damped system is one which moves from an initial displacement to the equilibrium state without overshoot, in minimum time. For example a simple pendulum suspended in a container of light oil might just drop from an elevated starting point to hang straight down without ever swinging up on the opposite side. An overdamped system behaves like a critically damped system except that it takes longer to reach equilibrium. For example a simple pendulum suspended in a container of honey would probably be overdamped