Oscillations are waves that vibrate back and forth. They can be either damped or undamped, which is the difference between whether they gradually die out over time or keep bouncing back to their original position without change. Damped oscillations require an outside force like friction to slow them down. This blog post will discuss both types of oscillation in more detail so you know how to use them correctly!
What are damped Oscillations?
Damped oscillations are waves that gradually die out over time. This happens when there is an outside force like friction slowing them down. Without this force, the oscillations would continue bouncing back and forth forever! Damped oscillations are often found in nature, such as water waves crashing on the shore or a swinging pendulum coming to a stop.
Damped oscillations were first studied by Galileo Galilei, who observed the swinging of a pendulum and noticed that it gradually came to a stop. He used this observation to develop his theory of inertia, which states that an object in motion will stay in motion unless acted on by an outside force. Damped oscillations can further be divided into two categories: underdamped oscillations and overdamped oscillations.
There are three types of damped oscillations, pure damping (simple harmonic motion), critical damping (oscillating system with no overshooting), and subcritical/supercritical bifurcation.
Underdamped oscillations are those in which the restoring force is less than the damping force, leading to a decay in amplitude over time. Overdamped oscillations are those in which the restoring force is greater than the damping force, resulting in little or no decay in amplitude over time.
What are undamped oscillations?
An undamped oscillation is a wave that bounces back and forth forever, without changing its amplitude or frequency. It can be thought of as an “out-of-control” situation because the object in question will continue vibrating until it wears out! An example would be throwing a ball up in the air and watching it come back down. The ball will keep bouncing back and forth until it eventually falls to the ground.
Undamped oscillations were first studied by Christiaan Huygens, who observed the swinging of a pendulum and noticed that it kept bouncing back to its original position. He used this observation to develop his theory of elasticity, which states that an object will return to its original shape after being deformed. The other examples of undamped oscillations are the transverse waves on a string and the sound waves emitted from a speaker.
The types of undamped oscillations are free and forced. A free oscillation is one that takes place when the restoring force (F) is in equilibrium with the inertial force (I). This only happens if there is no external disturbance to the system. A forced oscillation, on the other hand, is one that occurs when an externally applied force (F) causes a displacement from equilibrium. The most common type of forced oscillation is vibration, which is when an object moves back and forth sinusoidally about its equilibrium position.
Difference Between Damped and Undamped Oscillations
- Damped oscillations die out over time due to an outside force, while undamped oscillations continue bouncing back and forth forever
- Damped oscillations are often found in nature, while undamped oscillations are not as common
- The amplitude (height) of damped oscillations decreases over time, while the amplitude of undamped oscillations stays the same
- The frequency (how often the wave bounces back and forth) of damped oscillations decreases over time, while the frequency of undamped oscillations stays the same.
Damped vibrations occur when energy is drawn from the system. The amplitude of the wave will decrease over time. Meanwhile, Undamped vibrations mean that the amplitude of the wave does not change with time.