Oscillations of air-track glider

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The discussion revolves around calculating the number of oscillations of a damped air-track glider attached to a spring. The glider has a mass of 160 g, a spring constant of 4.40 N/m, and a damping constant of 2.40×10−2 kg/s. The initial amplitude is 23.0 cm, and the goal is to determine how many oscillations occur before the amplitude decays to e^-1 of its initial value. The damped oscillator equation includes both a decaying exponential and an oscillatory component, which are essential for solving the problem. Participants emphasize the need to integrate both aspects to find the total number of oscillations within the specified decay time.
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A 160 g air-track glider is attached to a spring with spring constant 4.40 N/m. The damping constant due to air resistance is 2.40×10−2 kg/s. The glider is pulled out 23.0 cm from equilibrium and released.

How many oscillations will it make during the time in which the amplitude decays to e^-1 of its initial value?

I have no clue how to approach this problems except that
x(t)=Ae^-bt/2m=Ae^-t/2tau
but how can I fin that amount of oscillations?
I'm confused and the dead lines in an hour
please help!
 
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Kalie said:
A 160 g air-track glider is attached to a spring with spring constant 4.40 N/m. The damping constant due to air resistance is 2.40×10−2 kg/s. The glider is pulled out 23.0 cm from equilibrium and released.

How many oscillations will it make during the time in which the amplitude decays to e^-1 of its initial value?

I have no clue how to approach this problems except that
x(t)=Ae^-bt/2m=Ae^-t/2tau
but how can I fin that amount of oscillations?
I'm confused and the dead lines in an hour
please help!
The damped oscillator equation for x(t) has a decaying exponential part and an oscillatory part (sine or cosine). You need both parts to do this problem.

http://hyperphysics.phy-astr.gsu.edu/Hbase/oscda.html
 

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