Undamped oscillation

What is Undamped oscillation

In undamped vibrations, no resistive force acts on the vibrating object. As the object oscillates, the energy in the object is continuously transformed from kinetic

energy to potential energy and back again, and the sum of kinetic and potential energy remains a constant value.

In practice, it’s extremely difficult to find undamped vibrations. For instance, even an object vibrating in air would lose energy over time due to air resistance.

• Let us consider an object undergoing simple harmonic motion. Here, the objet experiences a restoring force towards the equillibrium point, and the size of this force is proportional to displacement.• If the displacement of the object is given by x, then for an object with

mass m in simple harmonic motion, we can write:

Undamped oscillation• This is a differential equation. A solution to this equation can be written

in the form:

•

•

• If vibration is undamped, the object continues to oscillate sinusoidally.

Undamped oscillation

Difference Between Damped and Undamped Vibration

Presence of Resistive Forces

• In undamped vibrations, the object oscillates freely without any resistive force acting against its motion.• In damped vibrations, the object experiences resistive forces.

Energy Loss

• In undamped vibrations, the sum of kinetic and potential energies always gives the total energy of the oscillating object, and the value of its total energy does not change.• In damped vibrations, the total energy of the oscillating object

decreases over time. This energy is dissipated as the object does work against the resistive forces.

Value of the Damping Coefficient• For undamped vibrations, • For damped vibrations,

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