Damped Egg on a Spring
A 50.0- hard-boiled egg moves on the end of a spring with force constant . It is released with an amplitude 0.300 . A damping force acts on the egg. After it oscillates for 5.00 , the amplitude of the motion has decreased to 0.100 .
Part A
Calculate the magnitude of the damping coefficient .
Part A.1 How damped is it?
The system described above is ___________.
Hint A.1.a Hint not displayed
ANSWER:
 critically dampedoverdampedunderdamped
Hint A.2 What formula to use In this problem, the motion is described by the general equation for an underdamped oscillator, , where , is position, and is time. The displacement is thus a product of a oscillating cosine term and a damping term . This equation is the solution to the damped oscillator equation .
Part A.3 Find the amplitude
What is , the amplitude as a function of time? Use for the initial displacement of the system and for the mass of the egg.
Hint A.3.a Initial amplitude In the formula given in for the motion of the egg, is the initial amplitude of the system. This means that is a displacement at time .
Give your answer in terms of , , , and .
ANSWER:
 = A_0*e^(-b*t/(2*m))
Now evaluate and set your answer equal to 0.100 as given in the problem introduction. Finally, solve for .
Hint A.4 Solving for in Hint not displayed
Express the magnitude of the damping coefficient numerically in kilograms per second, to three significant figures.
ANSWER:
 = 0.022 kg/s
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