What is free vibration and forced vibration?

Free vibration and forced vibration are two types of oscillations or vibrations that occur in mechanical systems.

Free Vibration: Free vibration refers to the natural oscillation of a system in the absence of external forces or disturbances. When a system is subjected to an initial displacement or velocity and then left to oscillate on its own, it will exhibit free vibration. The motion is solely determined by the system's inherent characteristics, such as its mass, stiffness, and damping. The system will oscillate at its natural frequency, which depends on these characteristics. Examples of free vibration include a swinging pendulum, a vibrating guitar string after plucking, or a building swaying during an earthquake.

Forced Vibration: Forced vibration occurs when a system is subjected to external forces or excitations that continuously act upon it. The system responds to these external forces by oscillating at a frequency that may or may not be its natural frequency. The external force driving the vibration can be periodic, such as a harmonic force, or non-periodic, such as an impulse or random force. The system's response to the external force depends on the force's frequency and magnitude as well as the system's natural frequency and damping. Forced vibrations are commonly encountered in various engineering applications, such as machinery with rotating parts, vehicles moving over uneven surfaces, or bridges experiencing wind-induced vibrations.

In summary, free vibration is the natural oscillation of a system without external influences, while forced vibration is the response of a system to external forces or excitations.