The essential goal of this investigation was to break down the free oscillatory motion of dynamic systems and the powers related with the motion. This is the investigation of a free vibration of two states of a spring mass system that is un-damped and damped. Free vibration happens when a mechanical system is set in motion with an underlying info and permitted to vibrate unreservedly. Cases of this kind of vibration are pulling a kid back on a swing and lifting up or hitting a tuning fork and giving it a chance to ring. The mechanical system vibrates at least one of its regular frequencies and damps down to motionlessness. A definitive objective in the investigation of vibration is to decide its impact on the execution and security of...