Q12CQ
Question
Most harmonic oscillators are damped and, if undriven, eventually come to a stop. How is this observation related to the second law of thermodynamics?
Step-by-Step Solution
VerifiedThe change in amplitude of the damped oscillation increases the entropy (disorderness) of the system and this is in accordance with the second law of thermodynamics.
In the real world, oscillations are not perfectly simple harmonic oscillations. The friction of some sort or the other is usually present in the surroundings to dampen the motion so that it dies away eventually. Unless no driven force is acted the amplitude of the oscillation keeps on decreasing until it finally stops.
For example, a simple pendulum if made to oscillate in the real world will keep on interacting with the air molecules which in return will provide friction. As a result, the motion will become damped harmonic oscillation.
The second law of thermodynamics is related to the direction of natural processes. It states that any naturally occurring process will always lead to an increase in entropy in the universe. Entropy is a measurable physical property associated with the state of disorder, uncertainty, and randomness in the system.
A simple un-damped harmonic oscillator is an ordered symmetric system in which amplitude remains constant throughout. But in the real world, there are frictions in the surrounding which tend to destroy this orderliness of un-damped harmonic oscillators and thereby make them damped. Thus it is seen that in the real world, the un-damped oscillation tends to move toward disorders which means an increased entropy state. This is totally in accordance with the second law of thermodynamics.