A block having a weight of 8 lb is suspended from a spring having a stiffness k = 40 Ib/ft. If the block is pushed y = 0.2 ft upward from its equilibrium position and then released from rest. What is the natural frequency of the vibration? Assume that positive displacement is downward.

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.