Hey,

Forced and free vibrations are two concepts in the study of mechanical systems and oscillations:

1. Free Vibrations:

(a) Free vibrations occur when a system is allowed to oscillate on its own without any external force acting upon it after an initial disturbance.

(b) The oscillation happens at the natural frequency of the system, which is determined by its mass, stiffness, and damping properties.

(c) Examples of free vibrations include a pendulum swinging or a guitar string vibrating after being plucked.

2. Forced Vibrations:

(a) Forced vibrations occur when a system is subjected to an external force or excitation.

(b) The external force imposes a driving frequency on the system, which may or may not match its natural frequency.

(c) If the driving frequency matches the natural frequency, resonance can occur, resulting in large amplitude vibrations.

(d) Examples of forced vibrations include a car's suspension system responding to road bumps or a building swaying in response to wind or an earthquake.

In summary, free vibrations occur naturally without any external influence, while forced vibrations are induced by external forces acting on the system.

Hope this helps you.