Damping is the phenomenon of the decrease in the oscillations over time, due to the presence of resistive forces. The loss of energy during the oscillation due to resistive forces (e.g., friction) is known as damping and it results in a decrease in amplitude.
- In case of a damped oscillation, the amplitude of the oscillating body decreases exponentially.

Without any resistive force,such as friction or air resistance acting on an oscillating system, the oscillations will ideally continue forever. In the absence of resistive forces, no energy is dissipated which implies that the amplitude remains constant over time.
The frequency of oscillations also remains constant. This frequency is called the natural frequency, and the oscillations are known as free oscillations.

Types of damping:
- Light damping: The damping produced in an oscillating system is low and results in a gradual reduction of amplitude over time.
- Example: vibrating guitar strings, a ruler fixed at one end, a swing under air resistance.
- Displacement-time graph of light damping
- Critical damping: The oscillating system does not oscillate and the amount of damping is just enough to return the oscillating body to the equilibrium position in the shortest time period.
- Example: car suspension system, speedometer.
- Displacement-time graph of critical damping
- Heavy damping: It has the largest resistive force acting, and the system does not oscillate as in critical damping but takes a longer period of time to return to the equilibrium position.
- Example: swing doors in labs and malls.
- Displacement-time graph of heavy damping

Forced oscillation: When a periodic force is applied to an oscillating system, it is forced to vibrate at a frequency other than its natural frequency. This frequency is called driving frequency or forced frequency, and the motion accompanying such frequency is called forced oscillation.

Resonance is a phenomenon which occurs when the driving frequency of an oscillating object becomes equal to the natural frequency. That particular frequency is known as resonance frequency. At resonance, the oscillating system is capable of absorbing the energy most efficiently from the driver. Resonance results in the maximum amplitude of an oscillation.
- Some useful implications of resonance include magnetic resonance imaging (MRI), television and radio tuning, musical notes, etc.

14.03 - Damped Oscillations

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