Free Vibration

Vibrating system is modeled by a spring mass system, in its most simple form. Let us derive the equation of motion for a spring mass sysetm. One end of a spring of spring constant k is fixed and a mass m is attached at the other end.

The mass is being pulled by gravitation force W of magnitude mg. Due to this, spring stretches.

The free body diagram of the mass is shown in the middle of the figure. The mass is balanced due to gravitational force and spring force. If the static deflection of the spring is , then