Question

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

Answer 1

The period of the oscillator and the damping coefficient.

• t= 1.33s
• b = 0.0426 s^-1

What is the period of the oscillator and what determines the damping coefficient.?

Generally, the equation for is  mathematically given as

If we see cycles between the timestamps t= 0s and t= 4s, we may deduce that it completes three cycles each and every four seconds. Therefore, the amount of time required to complete one cycle of damping will be

t =4/3sec

t= 1.33s

Generally, the equation for amplitude is  mathematically given 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, An influence that acts either from inside an oscillatory system or onto it and has the effect of diminishing or stopping the system from oscillating is known as damping. In physical systems, damping is created by processes that dissipate the energy that is stored in the oscillation. These processes are called "damping agents.". Hence the damping coefficient is

b = 0.0426 s^-1

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