Damping Oscillations!

You may think of oscillations as something that goes on forever, and ever, and ever, and ever… Until the end of time, possibly? No! There are many reasons that may cause this oscillation motion to stop- this is called damping. 

A damping oscillation refers to an oscillatory motion in which the amplitude of the oscillation gradually decreases over time due to the loss of energy from the system. This motion is usually sinusoidal, which means that the graph of its displacement as a function of time is similar to a sine function. This reduction in amplitude happens because of resistive or dissipative forces such as friction, air resistance, or other forms of energy dissipation acting on the oscillating system. Most commonly, as you are swinging a pendulum, the bob or the thing that you are oscillating will interact with air particles, thereby reducing its speeds and causing it to come to rest. In terms of energy, the oscillation's energy diminishes until it eventually stops or settles at equilibrium. That’s why things don’t oscillate forever on Earth unless there is 0 air resistance! 

There are three different types of damping: 

• Underdamped oscillation: The system oscillates with an amplitude that decreases exponentially over time but continues to oscillate before coming to rest. This is common in many physical systems like a mass on a spring or a swinging pendulum.

• Critically damped oscillation: The system returns to equilibrium as quickly as possible without oscillating. This type of damping is often desirable in systems like car suspension to avoid oscillations after a disturbance.

• Overdamped oscillation: The system returns to equilibrium without oscillating but more slowly than in the critically damped case.

The three different types of damping can be quantified as a damping ratio ζ which evaluates the degree of damping. 

Underdamped: ζ = 0 

Critically: ζ = 1

Overdamped: ζ > 1

The degrees of the damping are also shown in this diagram below, see how quickly they return to equilibrium! 

In terms of examples of damping, there are too many! It’s all around us as we are on Earth! In space, it would be a completely different story without any frictional forces from any air particles. Once you allow something to oscillate, it will continue its motion unless you exert another force on it to stop the oscillation. A significant application of damping is in the use of vehicle suspension systems, where the oscillation system tries to absorb all shocks and stabilize the car’s handling. 

In order to change the damping ratio, physical properties such as the mass, surface area, and spring constant of the bob can be changed. Or else, you could also change the medium of the oscillation, where you could test out the time it takes for the oscillation to stop in different mediums such as air, water, or even oil! These are all great experiments to try out! 

To learn more about damping, please check out this YouTube video! 

References: 

Aakash.ac.in. (2025). Damped Oscillations - energy, practice problems, FAQs in physics: Definition, Types and Importance | AESL. [online] Available at: https://www.aakash.ac.in/important-concepts/physics/damped-oscillation.

BYJUS (n.d.). Damped Oscillation - Definition, Equations, Examples, Types. [online] BYJUS. Available at: https://byjus.com/jee/damped-oscillation/.

Mathworks.cn. (2025). The Physics of the Damped Harmonic Oscillator - MATLAB & Simulink Example. [online] Available at: https://ww2.mathworks.cn/help/symbolic/physics-damped-harmonic-oscillator.html [Accessed 2 May 2025].

Openstax (2016). 15.6: Damped Oscillations. [online] Physics LibreTexts. Available at: https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book:_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/15:_Oscillations/15.06:_Damped_Oscillations.

Science Buddies (2008). Simple Harmonic Motion in a Spring-Mass System. [online] Science Buddies. Available at: https://www.sciencebuddies.org/science-fair-projects/project-ideas/Phys_p064/physics/simple-harmonic-motion-springs.