Question

The y-position of a damped oscillator as a function of time is shown in the figure.

Answer 1

The length of time that an oscillator is allowed to oscillate, as well as its damping coefficient.

• t= 1.33s
• b = 0.0426 s^-1

What is the period of the oscillator, and what factors influence the amount of damping that it has?

In most situations, the equation may be expressed numerically as

When we look at the data and see that there are cycles between the timestamps t= 0s and t= 4s, we may conclude that it finishes three cycles once every four seconds. As a result, the length of time that is going to be necessary to finish one cycle of damping will be

t =4/3sec

t= 1.33s

In most situations, the equation for amplitude may be expressed analytically as

A=A_0e^{-bt}

Therefore

3=5e^{-12b}

$0.6=e^{-12b}$

Therefore

-0.511 = -12b lne

$b = 0.0426 s^{-1}$

In conclusion, damping refers to an influence that either operates from inside an oscillatory system or acts on it and has the consequence of reducing or halting the system from oscillating. This impact might occur from either side of the system. In physical systems, damping is produced by processes that cause the energy that is stored in an oscillation to be lost. These processes are called dissipative. The collective name for these processes is "damping agents." The damping coefficient may thus be written as

$b = 0.0426 s^-1$

Learn more about the damping coefficient by reading up on it.

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